Editing Numeric Quest (section)

=== Dirac quantum mechanics ===

;[http://code.haskell.org/~thielema/numeric-quest/QuantumVector.lhs QuantumVector.lhs]

:This is our attempt to model the abstract Dirac's formalism of Quantum Mechanics in Haskell.

:We recognize a quantum state as an abstract vector | x >, which can be represented in one of many possible bases -- similar to many alternative representations of a 3D vector in rotated systems of coordinates. A choice of a particular basis is controlled by a generic type variable, which can be any Haskell object -- providing that it supports a notion of equality and ordering. A state which is composed of many quantum subsystems, not necessarily of the same type, can be represented in a vector space considered to be a tensor product of the subspaces.

:With this abstract notion we proceed with Haskell definition of two vector spaces: Ket and its dual Bra. We demonstrate that both are properly defined according to the abstract mathematical definition of vector spaces. We then introduce inner product and show that our Bra and Ket can be indeed considered the vector spaces with inner product.

[[Category:Mathematics]]
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