Safe Haskell	Safe-Inferred
Language	Haskell98

QuantumVector

Documentation

class DiracVector a where Source #

Minimal complete definition

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

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

Instances details

Ord a => DiracVector (Bra a) Source #
Instance details Defined in QuantumVector Methods add :: 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 #
Instance details Defined in QuantumVector Methods add :: 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 #

type Scalar = Complex Double Source #

data Ket a Source #

Constructors

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

Instances

Instances details

(Show a, Eq a, Ord a) => Show (Ket a) Source #
Instance details Defined in QuantumVector Methods showsPrec :: Int -> Ket a -> ShowS # show :: Ket a -> String # showList :: [Ket a] -> ShowS #
(Eq a, Ord a) => Eq (Ket a) Source #
Instance details Defined in QuantumVector Methods (==) :: Ket a -> Ket a -> Bool # (/=) :: Ket a -> Ket a -> Bool #
Ord a => DiracVector (Ket a) Source #
Instance details Defined in QuantumVector Methods add :: 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

Instances details

(Show a, Eq a, Ord a) => Show (Bra a) Source #
Instance details Defined in QuantumVector Methods showsPrec :: Int -> Bra a -> ShowS # show :: Bra a -> String # showList :: [Bra a] -> ShowS #
(Eq a, Ord a) => Eq (Bra a) Source #
Instance details Defined in QuantumVector Methods (==) :: Bra a -> Bra a -> Bool # (/=) :: Bra a -> Bra a -> Bool #
Ord a => DiracVector (Bra a) Source #
Instance details Defined in QuantumVector Methods add :: 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 #

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

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

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

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

data Tuple a b Source #

Constructors

a :* b

Instances

Instances details

(Show a, Show b) => Show (Tuple a b) Source #
Instance details Defined in QuantumVector Methods showsPrec :: Int -> Tuple a b -> ShowS # show :: Tuple a b -> String # showList :: [Tuple a b] -> ShowS #
(Eq a, Eq b) => Eq (Tuple a b) Source #
Instance details Defined in QuantumVector Methods (==) :: Tuple a b -> Tuple a b -> Bool # (/=) :: Tuple a b -> Tuple a b -> Bool #
(Ord a, Ord b) => Ord (Tuple a b) Source #
Instance details Defined in QuantumVector 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 #