numeric-quest-0.2.0.2: Math and quantum mechanics

QuantumVector

# Documentation

class DiracVector a where Source #

Minimal complete definition

Methods

add :: a -> a -> a Source #

scale :: Scalar -> a -> a Source #

reduce :: a -> a Source #

basis :: a -> [a] Source #

components :: a -> [Scalar] Source #

compose :: [Scalar] -> [a] -> a Source #

dimension :: a -> Int Source #

norm :: a -> Double Source #

normalize :: a -> a Source #

Instances

 Ord a => DiracVector (Bra a) Source # Methodsadd :: Bra a -> Bra a -> Bra a Source #scale :: Scalar -> Bra a -> Bra a Source #reduce :: Bra a -> Bra a Source #basis :: Bra a -> [Bra a] Source #components :: Bra a -> [Scalar] Source #compose :: [Scalar] -> [Bra a] -> Bra a Source #dimension :: Bra a -> Int Source #norm :: Bra a -> Double Source #normalize :: Bra a -> Bra a Source # Ord a => DiracVector (Ket a) Source # Methodsadd :: Ket a -> Ket a -> Ket a Source #scale :: Scalar -> Ket a -> Ket a Source #reduce :: Ket a -> Ket a Source #basis :: Ket a -> [Ket a] Source #components :: Ket a -> [Scalar] Source #compose :: [Scalar] -> [Ket a] -> Ket a Source #dimension :: Ket a -> Int Source #norm :: Ket a -> Double Source #normalize :: Ket a -> Ket a Source #

data Ket a Source #

Constructors

 KetZero Ket a Scalar :|> (Ket a) (Ket a) :+> (Ket a)

Instances

 (Eq a, Ord a) => Eq (Ket a) Source # Methods(==) :: Ket a -> Ket a -> Bool #(/=) :: Ket a -> Ket a -> Bool # (Show a, Eq a, Ord a) => Show (Ket a) Source # MethodsshowsPrec :: Int -> Ket a -> ShowS #show :: Ket a -> String #showList :: [Ket a] -> ShowS # Ord a => DiracVector (Ket a) Source # Methodsadd :: Ket a -> Ket a -> Ket a Source #scale :: Scalar -> Ket a -> Ket a Source #reduce :: Ket a -> Ket a Source #basis :: Ket a -> [Ket a] Source #components :: Ket a -> [Scalar] Source #compose :: [Scalar] -> [Ket a] -> Ket a Source #dimension :: Ket a -> Int Source #norm :: Ket a -> Double Source #normalize :: Ket a -> Ket a Source #

(*>) :: (Ord a, Ord b) => Ket a -> Ket b -> Ket (Tuple a b) infixl 7 Source #

(|>) :: Ord a => Scalar -> Ket a -> Ket a infix 6 Source #

(+>) :: Ord a => Ket a -> Ket a -> Ket a infixl 5 Source #

reduceKet :: Ord a => Ket a -> Ket a Source #

ketBasis :: Ord a => Ket a -> [Ket a] Source #

toBra :: Ord a => Ket a -> Bra a Source #

data Bra a Source #

Constructors

 BraZero Bra a Scalar :<| (Bra a) (Bra a) :<+ (Bra a)

Instances

 (Eq a, Ord a) => Eq (Bra a) Source # Methods(==) :: Bra a -> Bra a -> Bool #(/=) :: Bra a -> Bra a -> Bool # (Show a, Eq a, Ord a) => Show (Bra a) Source # MethodsshowsPrec :: Int -> Bra a -> ShowS #show :: Bra a -> String #showList :: [Bra a] -> ShowS # Ord a => DiracVector (Bra a) Source # Methodsadd :: Bra a -> Bra a -> Bra a Source #scale :: Scalar -> Bra a -> Bra a Source #reduce :: Bra a -> Bra a Source #basis :: Bra a -> [Bra a] Source #components :: Bra a -> [Scalar] Source #compose :: [Scalar] -> [Bra a] -> Bra a Source #dimension :: Bra a -> Int Source #norm :: Bra a -> Double Source #normalize :: Bra a -> Bra a Source #

(<*) :: (Ord a, Ord b) => Bra a -> Bra b -> Bra (Tuple a b) infixl 7 Source #

(<|) :: Ord a => Scalar -> Bra a -> Bra a infix 6 Source #

(<+) :: Ord a => Bra a -> Bra a -> Bra a infixl 5 Source #

reduceBra :: Ord a => Bra a -> Bra a Source #

braBasis :: Ord a => Bra a -> [Bra a] Source #

toKet :: Ord a => Bra a -> Ket a Source #

(<>) :: Ord a => Bra a -> Ket a -> Scalar infix 4 Source #

d :: Eq a => a -> a -> Scalar Source #

closure :: (DiracVector a, DiracVector b) => (a -> b) -> a -> b Source #

(><) :: (DiracVector b, DiracVector a) => (a -> b) -> a -> b infix 5 Source #

label :: t -> Ket t1 -> Ket (t, t1) Source #

label' :: (Ord a, Ord b) => Ket (a, b) -> Ket b Source #

data Tuple a b Source #

Constructors

 a :* b

Instances

 (Eq b, Eq a) => Eq (Tuple a b) Source # Methods(==) :: Tuple a b -> Tuple a b -> Bool #(/=) :: Tuple a b -> Tuple a b -> Bool # (Ord b, Ord a) => Ord (Tuple a b) Source # Methodscompare :: Tuple a b -> Tuple a b -> Ordering #(<) :: Tuple a b -> Tuple a b -> Bool #(<=) :: Tuple a b -> Tuple a b -> Bool #(>) :: Tuple a b -> Tuple a b -> Bool #(>=) :: Tuple a b -> Tuple a b -> Bool #max :: Tuple a b -> Tuple a b -> Tuple a b #min :: Tuple a b -> Tuple a b -> Tuple a b # (Show a, Show b) => Show (Tuple a b) Source # MethodsshowsPrec :: Int -> Tuple a b -> ShowS #show :: Tuple a b -> String #showList :: [Tuple a b] -> ShowS #