Transformation theory (quantum mechanics)

# Transformation theory (quantum mechanics)

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The term transformation theory refers to a procedure used by P. A. M. Dirac in his early formulation of quantum theory
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

, from around 1927 .

The term is related to the famous wave-particle duality, according to which a particle
Elementary particle
In particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not known to be made up of smaller particles. If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which...

(a "small" physical object) may display either particle or wave aspects, depending on the observational situation. Or, indeed, a variety of intermediate aspects, as the situation demands.

This "transformation" idea also refers to the changes a physical object may undergo in the course of time, whereby it may "move" between "positions" in its Hilbert "space".

Remaining in full use today, it would be regarded as a topic in the mathematics of Hilbert space
Hilbert space
The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It extends the methods of vector algebra and calculus from the two-dimensional Euclidean plane and three-dimensional space to spaces with any finite or infinite number of dimensions...

, although technically speaking it is somewhat more general in scope. While the terminology is reminiscent of motion in ordinary space, the Hilbert space of a quantum object is more general, and holds its entire quantum state.