N6      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~        !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~None assumes radians coming in6theta=0 is positive x axis, output angle in radiansAn arrow9Rotate takes its angle in degrees, and rotates clockwise. A think arrow location of base of arrowdisplacement vectordisplacement vectorarrow thicknesslocation of base of arrowdisplacement vector   (c) Scott N. Walck 2016BSD3 (see LICENSE)Scott N. Walck <walck@lvc.edu> experimental Trustworthy)The state resulting from a measurement of spin angular momentum in the x direction on a spin-1/2 particle when the result of the measurement is hbar/2.The state resulting from a measurement of spin angular momentum in the x direction on a spin-1/2 particle when the result of the measurement is -hbar/2.The state resulting from a measurement of spin angular momentum in the y direction on a spin-1/2 particle when the result of the measurement is hbar/2.The state resulting from a measurement of spin angular momentum in the y direction on a spin-1/2 particle when the result of the measurement is -hbar/2.The state resulting from a measurement of spin angular momentum in the z direction on a spin-1/2 particle when the result of the measurement is hbar/2.The state resulting from a measurement of spin angular momentum in the z direction on a spin-1/2 particle when the result of the measurement is -hbar/2.The state resulting from a measurement of spin angular momentum in the direction specified by spherical angles theta (polar angle) and phi (azimuthal angle) on a spin-1/2 particle when the result of the measurement is hbar/2.The state resulting from a measurement of spin angular momentum in the direction specified by spherical angles theta (polar angle) and phi (azimuthal angle) on a spin-1/2 particle when the result of the measurement is -hbar/2.Dimension of a vector.+Scale a complex vector by a complex number.5Complex inner product. First vector gets conjugated.Length of a complex vector.4Return a normalized version of a given state vector. :Return a vector of probabilities for a given state vector.!"Conjugate the entries of a vector."2Construct a vector from a list of complex numbers.#0Produce a list of complex numbers from a vector.$The Pauli X matrix.%The Pauli Y matrix.&The Pauli Z matrix.'+Scale a complex matrix by a complex number.(Matrix product.)Matrix-vector product.*Vector-matrix product+ Conjugate transpose of a matrix.,;Construct a matrix from a list of lists of complex numbers.-9Produce a list of lists of complex numbers from a matrix..Size of a matrix./Apply a function to a matrix. Assumes the matrix is a normal matrix (a matrix with an orthonormal basis of eigenvectors).0Complex outer product16Build a pure-state density matrix from a state vector.2Trace of a matrix.34Normalize a density matrix so that it has trace one.4"The one-qubit totally mixed state.5Given a time step and a Hamiltonian matrix, produce a unitary time evolution matrix. Unless you really need the time evolution matrix, it is better to use 6z, which gives the same numerical results without doing an explicit matrix inversion. The function assumes hbar = 1.6Given a time step and a Hamiltonian matrix, advance the state vector using the Schrodinger equation. This method should be faster than using 5q since it solves a linear system rather than calculating an inverse matrix. The function assumes hbar = 1.7Given a Hamiltonian matrix, return a function from time to evolution matrix. Uses spectral decomposition. Assumes hbar = 1.8|The possible outcomes of a measurement of an observable. These are the eigenvalues of the matrix of the observable.9fGiven an obervable, return a list of pairs of possible outcomes and projectors for each outcome.:|Given an observable and a state vector, return a list of pairs of possible outcomes and probabilites for each outcome.;cForm an orthonormal list of complex vectors from a linearly independent list of complex vectors.0  state vectorvector of probabilities!"#$%&'()*+,-./0123456789:;<=. !"#$%&'()*+,-./0123456789:;. ;!"#$%&'()*+,-./0123456789:/ !"#$%&'()*+,-./0123456789:;<=(c) Scott N. Walck 2016BSD3 (see LICENSE)Scott N. Walck <walck@lvc.edu> experimentalSafe9;<=?CAn orthonormal basis of kets.GGThe adjoint operation on complex numbers, kets, bras, and operators.IGeneric multiplication including inner product, outer product, operator product, and whatever else makes sense. No conjugation takes place in this operation.K5A bra vector describes the state of a quantum system.L`An operator describes an observable (a Hermitian operator) or an action (a unitary operator).M5A ket vector describes the state of a quantum system.PCMake an orthonormal basis from a list of linearly independent kets.SfState of a spin-1/2 particle if measurement in the x-direction would give angular momentum +hbar/2.TfState of a spin-1/2 particle if measurement in the x-direction would give angular momentum -hbar/2.UfState of a spin-1/2 particle if measurement in the y-direction would give angular momentum +hbar/2.VfState of a spin-1/2 particle if measurement in the y-direction would give angular momentum -hbar/2.WfState of a spin-1/2 particle if measurement in the z-direction would give angular momentum +hbar/2.XfState of a spin-1/2 particle if measurement in the z-direction would give angular momentum -hbar/2.YState of a spin-1/2 particle if measurement in the n-direction, described by spherical polar angle theta and azimuthal angle phi, would give angular momentum +hbar/2.ZState of a spin-1/2 particle if measurement in the n-direction, described by spherical polar angle theta and azimuthal angle phi, would give angular momentum -hbar/2.["The orthonormal basis composed of S and T.\"The orthonormal basis composed of U and V.]"The orthonormal basis composed of W and X.^`Given spherical polar angle theta and azimuthal angle phi, the orthonormal basis composed of Y theta phi and Z theta phi._The Pauli X operator.`The Pauli Y operator.aThe Pauli Z operator.bZPauli operator for an arbitrary direction given by spherical coordinates theta and phi.cGAlternative definition of Pauli operator for an arbitrary direction.dGiven a time step and a Hamiltonian operator, produce a unitary time evolution operator. Unless you really need the time evolution operator, it is better to use ez, which gives the same numerical results without doing an explicit matrix inversion. The function assumes hbar = 1.eGiven a time step and a Hamiltonian operator, advance the state ket using the Schrodinger equation. This method should be faster than using dq since it solves a linear system rather than calculating an inverse matrix. The function assumes hbar = 1.f~The possible outcomes of a measurement of an observable. These are the eigenvalues of the operator of the observable.gfGiven an obervable, return a list of pairs of possible outcomes and projectors for each outcome.hyGiven an observable and a state ket, return a list of pairs of possible outcomes and probabilites for each outcome.MForm an orthonormal list of kets from a list of linearly independent kets.N>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~,>?@BACDFEGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefgh,ONMKLSTUVWXYZ_`abcde>?fghIJGHDEF@ABCPRQ[\]^C>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~J7(c) Scott N. Walck 2016BSD3 (see LICENSE)Scott N. Walck <walck@lvc.edu> experimental Trustworthy/A beam of randomly oriented spin-1/2 particles.+Return the intensities of a stack of beams.+Remove the most recent beam from the stack. Return the number of beams in a .3Interchange the two most recent beams on the stack.Given angles describing the orientation of the splitter, removes an incoming beam from the stack and replaces it with two beams, a spin-up and a spin-down beam. The spin-down beam is the most recent beam on the stack.sGiven angles describing the orientation of the recombiner, returns a single beam from an incoming pair of beams.Given angles describing the direction of a uniform magnetic field, and given an angle describing the product of the Larmor frequency and the time, return an output beam from an input beam.,A Stern-Gerlach splitter in the x direction.,A Stern-Gerlach splitter in the y direction.,A Stern-Gerlach splitter in the z direction.Given an angle in radians describing the product of the Larmor frequency and the time, apply a magnetic in the x direction to the most recent beam on the stack.Given an angle in radians describing the product of the Larmor frequency and the time, apply a magnetic in the y direction to the most recent beam on the stack.Given an angle in radians describing the product of the Larmor frequency and the time, apply a magnetic in the z direction to the most recent beam on the stack..A Stern-Gerlach recombiner in the x direction..A Stern-Gerlach recombiner in the y direction..A Stern-Gerlach recombiner in the z direction.0Filter for spin-up particles in the x direction.2Filter for spin-down particles in the x direction.0Filter for spin-up particles in the z direction.2Filter for spin-down particles in the z direction.$#(c) Scott N. Walck 2012-2014BSD3 (see LICENSE)Scott N. Walck <walck@lvc.edu> experimentalSafeGiven an initial bracketing of a root (an interval (a,b) for which f(a) f(b) <= 0), produce a bracket of arbitrary smallness.4Given a bracketed root, return a half-width bracket.mFind a single root in a bracketed region. The algorithm continues until it exhausts the precision of a ). This could cause the function to hang.Find a list of roots for a function over a given range. First parameter is the initial number of intervals to use to find the roots. If roots are closely spaced, this number of intervals may need to be large.yFind a list of roots for a function over a given range. There are no guarantees that all roots will be found. Uses  with 1000 intervals.desired accuracyfunctioninitial bracket final bracketfunctionoriginal bracket new bracketfunctioninitial bracketapproximate root"initial number of intervals to usefunctionrange over which to search list of rootsfunctionrange over which to search list of roots(c) Scott N. Walck 2012-2014BSD3 (see LICENSE)Scott N. Walck <walck@lvc.edu> experimental Trustworthy:Composite Trapezoid RuleComposite Simpson's RuleFnumber of intervals (one less than the number of function evaluations) lower limit upper limitfunction to be integrateddefinite integralKnumber of half-intervals (one less than the number of function evaluations) lower limit upper limitfunction to be integrateddefinite integral(c) Scott N. Walck 2012-2014BSD3 (see LICENSE)Scott N. Walck <walck@lvc.edu> experimentalSafe A type for vectors. x component y component z component3Form a vector by giving its x, y, and z components.Cross product.Unit vector in the x direction.Unit vector in the y direction.Unit vector in the z direction.  x component y component z component 7 (c) Scott N. Walck 2012-2014BSD3 (see LICENSE)Scott N. Walck <walck@lvc.edu> experimentalSafe The zero vector.!The additive inverse of a vector.Sum of a list of vectors.Vector addition.Vector subtraction.YScalar multiplication, where the scalar is on the left and the vector is on the right.YScalar multiplication, where the scalar is on the right and the vector is on the left.!Division of a vector by a scalar.Dot product of two vectors.Magnitude of a vector.  667777(c) Scott N. Walck 2011-2014BSD3 (see LICENSE)Scott N. Walck <walck@lvc.edu> experimental TrustworthyDR    (c) Scott N. Walck 2012-2014BSD3 (see LICENSE)Scott N. Walck <walck@lvc.edu> experimental Trustworthy9;AA coordinate system is a function from three parameters to space.tSometimes we want to be able to talk about a field without saying whether it is a scalar field or a vector field.?A vector field associates a vector with each position in space.?A scalar field associates a number with each position in space.A displacement is a vector.\A type for position. Position is not a vector because it makes no sense to add positions.+Add two scalar fields or two vector fields.:The Cartesian coordinate system. Coordinates are (x,y,z).The cylindrical coordinate system. Coordinates are (s,phi,z), where s is the distance from the z axis and phi is the angle with the x axis.The spherical coordinate system. Coordinates are (r,theta,phi), where r is the distance from the origin, theta is the angle with the z axis, and phi is the azimuthal angle.vA helping function to take three numbers x, y, and z and form the appropriate position using Cartesian coordinates.zA helping function to take three numbers s, phi, and z and form the appropriate position using cylindrical coordinates.|A helping function to take three numbers r, theta, and phi and form the appropriate position using spherical coordinates.DReturns the three Cartesian coordinates as a triple from a position.FReturns the three cylindrical coordinates as a triple from a position.DReturns the three spherical coordinates as a triple from a position.5Displacement from source position to target position.#Shift a position by a displacement.An object is a map into .A field is a map from . The vector field in which each point in space is associated with a unit vector in the direction of increasing spherical coordinate r, while spherical coordinates theta and phi are held constant. Defined everywhere except at the origin. The unit vector  points in different directions at different points in space. It is therefore better interpreted as a vector field, rather than a vector.The vector field in which each point in space is associated with a unit vector in the direction of increasing spherical coordinate theta, while spherical coordinates r and phi are held constant. Defined everywhere except on the z axis.-The vector field in which each point in space is associated with a unit vector in the direction of increasing (cylindrical or spherical) coordinate phi, while cylindrical coordinates s and z (or spherical coordinates r and theta) are held constant. Defined everywhere except on the z axis.The vector field in which each point in space is associated with a unit vector in the direction of increasing cylindrical coordinate s, while cylindrical coordinates phi and z are held constant. Defined everywhere except on the z axis.The vector field in which each point in space is associated with a unit vector in the direction of increasing Cartesian coordinate x, while Cartesian coordinates y and z are held constant. Defined everywhere.The vector field in which each point in space is associated with a unit vector in the direction of increasing Cartesian coordinate y, while Cartesian coordinates x and z are held constant. Defined everywhere.The vector field in which each point in space is associated with a unit vector in the direction of increasing Cartesian coordinate z, while Cartesian coordinates x and y are held constant. Defined everywhere. x coordinate y coordinate z coordinate s coordinatephi coordinate z coordinate r coordinatetheta coordinatephi coordinatesource positiontarget position (c) Scott N. Walck 2012-2014BSD3 (see LICENSE)Scott N. Walck <walck@lvc.edu> experimental Trustworthy)The x Cartesian coordinate of a position.)The y Cartesian coordinate of a position.:The z Cartesian (or cylindrical) coordinate of a position.dThe s cylindrical coordinate of a position. This is the distance of the position from the z axis.The phi cylindrical (or spherical) coordinate of a position. This is the angle from the positive x axis to the projection of the position onto the xy plane.bThe r spherical coordinate of a position. This is the distance of the position from the origin.lThe theta spherical coordinate of a position. This is the angle from the positive z axis to the position.   (c) Scott N. Walck 2012-2014BSD3 (see LICENSE)Scott N. Walck <walck@lvc.edu> experimental Trustworthy}Specification of a coordinate system requires a map from coordinates into space, and a map from space into coordinates.!a map from coordinates into space!a map from space into coordinates(The standard Cartesian coordinate system*The standard cylindrical coordinate system(The standard spherical coordinate systemDefine a new coordinate system in terms of an existing one. First parameter is a map from old coordinates to new coordinates. Second parameter is the inverse map from new coordinates to old coordinates.(x',y',z') = f(x,y,z)(x,y,z) = g(x',y',z')old coordinate system (c) Scott N. Walck 2012-2014BSD3 (see LICENSE)Scott N. Walck <walck@lvc.edu> experimental Trustworthy:DRR is a parametrized function into three-space, an initial limit, and a final limit.&function from one parameter into spacestarting value of the parameterending value of the parameter4A dotted line integral. Convenience function for .DCalculates integral vf x dl over curve. Convenience function for .<A dotted line integral, performed in an unsophisticated way.ACalculates integral vf x dl over curve in an unsophisticated way.GCalculates integral f dl over curve, where dl is a scalar line element."Reparametrize a curve from 0 to 1.Concatenate two curves.=Concatenate a list of curves. Parametrizes curves equally.Reverse a curve.0Evaluate the position of a curve at a parameter. Shift a curve by a displacement.5The straight-line curve from one position to another.}Quadratic approximation to vector field. Quadratic approximation to curve. Composite strategy. Dotted line integral.~Quadratic approximation to vector field. Quadratic approximation to curve. Composite strategy. Crossed line integral.Nnumber of half-intervals (one less than the number of function evaluations) vector fieldcurve to integrate over scalar resultNnumber of half-intervals (one less than the number of function evaluations) vector fieldcurve to integrate over vector resultnumber of intervals vector fieldcurve to integrate over scalar resultnumber of intervals vector fieldcurve to integrate over vector resultnumber of intervalsscalar or vector fieldcurve to integrate overscalar or vector resultgo first along this curvethen along this curveto produce this new curve the curve the parameter4position of the point on the curve at that parameteramount to shiftoriginal curve shifted curvestarting positionending positionstraight-line curvevector field lowvector field midvector field high dl low to middl mid to highquadratic approximationNnumber of half-intervals (one less than the number of function evaluations) vector fieldcurve to integrate over scalar resultvector field lowvector field midvector field high dl low to middl mid to highquadratic approximationNnumber of half-intervals (one less than the number of function evaluations) vector fieldcurve to integrate over vector result(c) Scott N. Walck 2011-2014BSD3 (see LICENSE)Scott N. Walck <walck@lvc.edu> experimentalSafeAn ( with a given label at a given position.An ! that requests postscript output.An ! giving the postscript file name.An example of the use of . See the source code.An example of the use of  and . See the source code.*Plot a Curve in the xy plane using Gnuplot(c) Scott N. Walck 2012-2014BSD3 (see LICENSE)Scott N. Walck <walck@lvc.edu> experimental TrustworthyDRSurface is a parametrized function from two parameters to space, lower and upper limits on the first parameter, and lower and upper limits for the second parameter (expressed as functions of the first parameter).-function from two parameters (s,t) into spaces_ls_ut_l(s) t_u(s) &A unit sphere, centered at the origin. 2A sphere with given radius centered at the origin. $Sphere with given radius and center. 8The upper half of a unit sphere, centered at the origin.1A disk with given radius, centered at the origin.<A plane surface integral, in which area element is a scalar.=A dotted surface integral, in which area element is a vector."Shift a surface by a displacement.     *number of intervals for first parameter, s+number of intervals for second parameter, t'the scalar or vector field to integrate#the surface over which to integratethe resulting scalar or vector*number of intervals for first parameter, s+number of intervals for second parameter, tthe vector field to integrate#the surface over which to integratethe resulting scalar                (c) Scott N. Walck 2012-2014BSD3 (see LICENSE)Scott N. Walck <walck@lvc.edu> experimental TrustworthyDRPVolume is a parametrized function from three parameters to space, lower and upper limits on the first parameter, lower and upper limits for the second parameter (expressed as functions of the first parameter), and lower and upper limits for the third parameter (expressed as functions of the first and second parameters).#function from 3 parameters to spaces_as_bt_a(s)t_b(s)u_a(s,t)u_b(s,t)$A unit ball, centered at the origin.IA unit ball, centered at the origin. Specified in Cartesian coordinates.1A ball with given radius, centered at the origin."Ball with given radius and center.1Upper half ball, unit radius, centered at origin. Cylinder with given radius and height. Circular base of the cylinder is centered at the origin. Circular top of the cylinder lies in plane z = h.!A volume integral n+1 points"!Shift a volume by a displacement.radiuscenter!ball with given radius and center !-number of intervals for first parameter (s)-number of intervals for second parameter (t)-number of intervals for third parameter (u)scalar or vector field the volumescalar or vector result" !" "! !"(c) Scott N. Walck 2012-2014BSD3 (see LICENSE)Scott N. Walck <walck@lvc.edu> experimental Trustworthy #A current distribution is a line current (current through a wire), a surface current, a volume current, or a combination of these. The D describes a surface current density or a volume current density.$current through a wire%! is surface current density (A/m)&" is volume current density (A/m^2)'$combination of current distributions()Electric current, in units of Amperes (A))TMagnetic field produced by a line current (current through a wire). The function ,R calls this function to evaluate the magnetic field produced by a line current.*>Magnetic field produced by a surface current. The function , calls this function to evaluate the magnetic field produced by a surface current. This function assumes that surface current density will be specified parallel to the surface, and does not check if that is true.+=Magnetic field produced by a volume current. The function ,T calls this function to evaluate the magnetic field produced by a volume current.,The magnetic field produced by a current distribution. This is the simplest way to find the magnetic field, because it works for any current distribution (line, surface, volume, or combination).-GThe magnetic flux through a surface produced by a current distribution. #$%&'()current (in Amps)geometry of the line currentmagnetic field (in Tesla)*surface current densitygeometry of the surface currentmagnetic field (in T)+volume current densitygeometry of the volume currentmagnetic field (in T),- #$%&'()*+,- (#$%&',)*+-#$%&'()*+,-(c) Scott N. Walck 2014BSD3 (see LICENSE)Scott N. Walck <walck@lvc.edu> experimental Trustworthy9:;DR .An evolution method is a way of approximating the state after advancing a finite interval in the independent variable (time) from a given state./A (numerical) solution method is a way of converting an initial value problem into a list of states (a solution). The list of states need not be equally spaced in time.0PAn initial value problem is a differential equation along with an initial state.1;A differential equation expresses how the dependent variables (state) change with the independent variable (time). A differential equation is specified by giving the (time) derivative of the state as a function of the state. The (time) derivative of a state is an element of the associated vector space.2OThe scalars of the associated vector space can be thought of as time intervals.3An instance of 3Q is a data type that can serve as the state of some system. Alternatively, a 3M is a collection of dependent variables for a differential equation. A 3 has an associated vector space for the (time) derivatives of the state. The associated vector space is a linearized version of the 3.4Associated vector space5Subtract points6Point plus vector7Point minus vector8Given an evolution method and a time step, return the solution method which applies the evolution method repeatedly with with given time step. The solution method returned will produce an infinite list of states.9tThe Euler method is the simplest evolution method. It increments the state by the derivative times the time step.?PPosition is not a vector, but displacement (difference in position) is a vector..differential equation time interval initial state evolved state/0123456789:;<=>?@A ./0123456789 34567210./89./0123456789:;<=>?@A566676(c) Scott N. Walck 2012-2014BSD3 (see LICENSE)Scott N. Walck <walck@lvc.edu> experimental Trustworthy:B(Take a single 4th-order Runge-Kutta stepCOSolve a first-order system of differential equations with 4th-order Runge-KuttaBCBCBCBC(c) Scott N. Walck 2014BSD3 (see LICENSE)Scott N. Walck <walck@lvc.edu> experimental TrustworthyDRDyAn acceleration function gives a list of accelerations (one for each particle) as a function of the system's state.EjThe state of a system of many particles is given by the current time and a list of one-particle states.FAn acceleration function gives a pair of accelerations (one for particle 1, one for particle 2) as a function of the system's state.GThe state of a system of two particles is given by the current time, the position and velocity of particle 1, and the position and velocity of particle 2.HdAn acceleration function gives the particle's acceleration as a function of the particle's state.IThe state of a system of one particle is given by the current time, the position of the particle, and the velocity of the particle. Including time in the state like this allows us to have time-dependent forces.JBThe associated vector space for the state of a single particle.LlThe state of a single particle is given by the position of the particle and the velocity of the particle.P|An acceleration function gives the particle's acceleration as a function of the particle's state. The specification of this function is what makes one single-particle mechanics problem different from another. In order to write this function, add all of the forces that act on the particle, and divide this net force by the particle's mass. (Newton's second law).QVA simple one-particle state, to get started quickly with mechanics of one particle.R Velocity of a particle (in m/s).SA time step (in s).T Time (in s).UGTime derivative of state for a single particle with a constant mass.VSingle Runge-Kutta stepWGTime derivative of state for a single particle with a constant mass.XSingle Runge-Kutta stepYList of system statesZATime derivative of state for two particles with constant mass.[/Single Runge-Kutta step for two-particle system\BTime derivative of state for many particles with constant mass.]0Single Runge-Kutta step for many-particle systemDEFGHIJKLMNOPQRSTU&acceleration function for the particledifferential equationV&acceleration function for the particle time step initial statestate after one time stepW&acceleration function for the particledifferential equationX&acceleration function for the particle time step initial statestate after one time stepY&acceleration function for the particle time step initial statestate after one time stepZ'acceleration function for two particlesdifferential equation[acceleration function time step initial statestate after one time step\(acceleration function for many particlesdifferential equation]acceleration function time step initial statestate after one time step^_`DEFGHIJKLMNOPQRSTUVWXYZ[\]TSRQPUVLMNOJKIHWXYGFZ[ED\]DEFGHIJKLMNOPQRSTUVWXYZ[\]^_`NonecMake a  object from a .dMake a  object from a .eDisplay a vector field.f$A displayable VisObject for a curve.g(Place a vector at a particular position.hA VisObject arrow from a vector cdecolor for the vector field scale factor#list of positions to show the fieldvector field to displaythe displayable objectfgh in radians in radianscdefghcdhgef cdefgh(c) Scott N. Walck 2011-2014BSD3 (see LICENSE)Scott N. Walck <walck@lvc.edu> experimental TrustworthykA charge distribution is a point charge, a line charge, a surface charge, a volume charge, or a combination of these. The \ describes a linear charge density, a surface charge density, or a volume charge density.l point chargem is linear charge density (C/m)n" is surface charge density (C/m^2)o! is volume charge density (C/m^3)p#combination of charge distributionsq)Electric charge, in units of Coulombs (C)r-Total charge (in C) of a charge distribution.s;Electric field produced by a point charge. The function wR calls this function to evaluate the electric field produced by a point charge.t:Electric field produced by a line charge. The function wQ calls this function to evaluate the electric field produced by a line charge.u=Electric field produced by a surface charge. The function wT calls this function to evaluate the electric field produced by a surface charge.v<Electric field produced by a volume charge. The function wS calls this function to evaluate the electric field produced by a volume charge.wThe electric field produced by a charge distribution. This is the simplest way to find the electric field, because it works for any charge distribution (point, line, surface, volume, or combination).xFThe electric flux through a surface produced by a charge distribution.yaElectric potential from electric field, given a position to be the zero of electric potential.zElectric potential produced by a charge distribution. The position where the electric potential is zero is taken to be infinity.klmnopqrscharge (in Coulombs)of point chargeelectric field (in V/m)tlinear charge density lambdageometry of the line chargeelectric field (in V/m)usurface charge density sigmageometry of the surface chargeelectric field (in V/m)vvolume charge density rhogeometry of the volume chargeelectric field (in V/m)wxy)position where electric potential is zeroelectric fieldelectric potentialzcharge (in Coulombs)of point chargeelectric potentiallinear charge density lambdageometry of the line chargeelectric potentialsurface charge density sigmageometry of the surface chargeelectric potentialvolume charge density rhogeometry of the volume chargeelectric potentialklmnopqrstuvwxyzqklmnoprwstuvxyzklmnopqrstuvwxyz(c) Scott N. Walck 2014BSD3 (see LICENSE)Scott N. Walck <walck@lvc.edu> experimental Trustworthy       !"#$%&'(,-./0123456789BCDEFGHIJKLMNOPQRSTUVWXYZ[\]cdefghklmnopqrwxyzTSRQPUVLMNOJKIHWXYGFZ[ED\]qklmnopr(#$%&'wxyz,-        "!34567210./89BC cdhgef(c) Scott N. Walck 2016BSD3 (see LICENSE)Scott N. Walck <walck@lvc.edu> experimentalNone { A Vis object.|QConvert a 2x1 complex state vector for a qubit into Bloch (x,y,z) coordinates.}6Convert a qubit ket into Bloch (x,y,z) coordinates.~ A static { for the state of a qubit.<Display a qubit state vector as a point on the Bloch Sphere.8Given a Bloch vector as a function of time, return a { as a function of time.qGiven a sample rate, initial qubit state vector, and state propagation function, produce a simulation. The X in the state propagation function is the time since the beginning of the simulation.nGiven a sample rate, initial qubit state ket, and state propagation function, produce a simulation. The X in the state propagation function is the time since the beginning of the simulation.GProduce a state propagation function from a time-dependent Hamiltonian.GProduce a state propagation function from a time-dependent Hamiltonian.ZGiven an initial qubit state and a time-dependent Hamiltonian, produce a visualization.XGiven an initial qubit ket and a time-dependent Hamiltonian, produce a visualization.MHamiltonian for nuclear magnetic resonance. Explain omega0, omegaR, omega.{|}~ {|}~ {|}~{|}~ !"#!"$!"%!"&!"'!()!(*!(+!(,!(-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_3`a<bc?@defIghi#jkOl456789:;mnopEFGqrsWYZ[tuvwxyz{|}~ - + ) , * & $ % ' #                 !"#$%&'()*+,-./0123456789:;<=>?@ABCDEEFFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~\ghi       ,learn-physics-0.6.0.2-Cd6fzLZXtXaHeTU5wiJG5kPhysics.Learn.QuantumMatPhysics.Learn.CarrotVecPhysics.Learn.Visual.GlossToolsPhysics.Learn.KetPhysics.Learn.BeamStackPhysics.Learn.RootFinding!Physics.Learn.CompositeQuadraturePhysics.Learn.CommonVecPhysics.Learn.SimpleVecPhysics.Learn.PositionPhysics.Learn.CoordinateFieldsPhysics.Learn.CoordinateSystemPhysics.Learn.CurvePhysics.Learn.Visual.PlotToolsPhysics.Learn.SurfacePhysics.Learn.VolumePhysics.Learn.CurrentPhysics.Learn.StateSpacePhysics.Learn.RungeKuttaPhysics.Learn.MechanicsPhysics.Learn.Visual.VisToolsPhysics.Learn.ChargePhysics.Learn.BlochSphere 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