Physics:Quantum Matrix mechanics
Matrix mechanics is a Book I topic in the Quantum Collection. 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.[1] Matrix mechanics is important because it made noncommuting observables the basic language of quantum theory. Instead of picturing electron orbits, it represents measurable quantities by arrays or operators whose multiplication order can matter. This formulation is equivalent to wave mechanics but remains especially natural for spin systems, finite-dimensional Hilbert spaces, and quantum information.
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:
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[2], 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.
See also
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References
- ↑ Heisenberg, Werner (1925). "Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen". Zeitschrift für Physik 33: 879-893. doi:10.1007/BF01328377.
- ↑ Dirac, Paul A. M. (1981). The Principles of Quantum Mechanics (4th revised ed.). New York: Oxford University Press. ISBN 0-19-852011-5.