| Copyright | (c) Scott N. Walck 2015-2016 |
|---|---|
| License | BSD3 (see LICENSE) |
| Maintainer | Scott N. Walck <walck@lvc.edu> |
| Stability | experimental |
| Safe Haskell | Trustworthy |
| Language | Haskell98 |
Physics.Learn.Schrodinger1D
Description
This module contains functions to solve the (time dependent) Schrodinger equation in one spatial dimension for a given potential function.
- freeV :: Double -> Double
- harmonicV :: Double -> Double -> Double
- squareWell :: Double -> Double -> Double -> Double
- doubleWell :: Double -> Double -> Double -> Double
- stepV :: Double -> Double -> Double
- wall :: Double -> Double -> Double -> Double -> Double
- harm :: Int -> Double -> C
- coherent :: Double -> Double -> Complex Double -> Double -> Complex Double
- gaussian :: Double -> Double -> Double -> Complex Double
- movingGaussian :: Double -> Double -> Double -> Double -> Complex Double
- stateVectorFromWavefunction :: R -> R -> Int -> (R -> C) -> Vector C
- hamiltonianMatrix :: R -> R -> Int -> R -> R -> (R -> R) -> Matrix C
- expectX :: Vector C -> Vector R -> R
- picture :: (Double, Double) -> [Double] -> Vector C -> Picture
Potentials
Free potential. The potential energy is zero everywhere.
Harmonic potential. This is the potential energy of a linear spring.
Arguments
| :: Double | well width |
| -> Double | energy height of well |
| -> Double | position |
| -> Double | potential energy |
Finite square well potential. Potential is zero inside the well, and constant outside the well. Well is centered at the origin.
Arguments
| :: Double | width (for both wells and well separation) |
| -> Double | energy height of barrier between wells |
| -> Double | position |
| -> Double | potential energy |
A double well potential. Potential energy is a quartic function of position that gives two wells, each approximately harmonic at the bottom of the well.
Arguments
| :: Double | energy height of barrier (to the right of origin) |
| -> Double | position |
| -> Double | potential energy |
A step barrier potential. Potential is zero to left of origin.
Arguments
| :: Double | thickness of wall |
| -> Double | energy height of barrier |
| -> Double | position of center of barrier |
| -> Double | position |
| -> Double | potential energy |
A potential barrier with thickness and height.
Initial wavefunctions
Arguments
| :: Int | nonnegative integer n identifying stationary state |
| -> Double | x sqrt(hbar(m * omega)), i.e. position in units of sqrt(hbar/(m * omega)) |
| -> C | complex amplitude |
Harmonic oscillator stationary state
Utilities
stateVectorFromWavefunction Source
Arguments
| :: R | lowest x |
| -> R | highest x |
| -> Int | dimension of state vector |
| -> (R -> C) | wavefunction |
| -> Vector C | state vector |
Transform a wavefunction into a state vector.