Safe Haskell	Safe
Language	Haskell98

QuantumVector

Documentation

class DiracVector a where #

Minimal complete definition

add, scale, reduce, basis, components, compose, norm

Methods

add :: a -> a -> a #

scale :: Scalar -> a -> a #

reduce :: a -> a #

basis :: a -> [a] #

components :: a -> [Scalar] #

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

dimension :: a -> Int #

norm :: a -> Double #

normalize :: a -> a #

Instances

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

type Scalar = Complex Double #

data Ket a #

Constructors

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

Instances

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

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

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

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

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

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

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

data Bra a #

Constructors

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

Instances

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

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

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

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

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

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

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

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

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

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

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

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

rot :: Ket Int -> Ket (Int, Int) #

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

rot' :: Ket (Int, Int) -> Ket Int #

showsScalar :: (Show t, RealFloat t) => Int -> Complex t -> String -> String #

data Tuple a b #

Constructors

a :* b

Instances

(Eq b, Eq a) => Eq (Tuple a b) #
Methods (==) :: Tuple a b -> Tuple a b -> Bool # (/=) :: Tuple a b -> Tuple a b -> Bool #
(Ord b, Ord a) => Ord (Tuple a b) #
Methods compare :: 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) #
Methods showsPrec :: Int -> Tuple a b -> ShowS # show :: Tuple a b -> String # showList :: [Tuple a b] -> ShowS #