Physics:Quantum Matrix mechanics

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Matrix mechanics represents observables by arrays or operators whose order may matter.

Matrix mechanics is a formulation of quantum mechanics in which physical quantities are represented by matrices or operators. It was developed by Werner Heisenberg, Max Born, and Pascual Jordan in 1925.

Description

In matrix mechanics, observables such as position, momentum, and energy are represented by mathematical objects that do not always commute. The order of multiplication can matter:

$AB\ne BA$

This non-commutative structure is one of the mathematical roots of the uncertainty principle.

Matrix mechanics was later shown to be equivalent to wave mechanics, but it remains a natural language for spin, finite-dimensional systems, quantum information, and operator methods.

Historical names

• Werner Heisenberg introduced the first form of matrix mechanics.
• Max Born and Pascual Jordan recognized and developed the matrix structure of the theory.

Related concepts

• Physics:Quantum mechanics
• Physics:Quantum Commutator
• Physics:Quantum Uncertainty principle
• Physics:Quantum Hamiltonian
• quantum operators

References

• Heisenberg, W. (1925). "Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen". Zeitschrift für Physik 33: 879-893. doi:10.1007/BF01328377. 
• "Matrix mechanics". https://www.britannica.com/science/matrix-mechanics. 

Author: Harold Foppele