Heisenberg's matrix mechanics equivalent to Schrödinger's wave mechanics from "summary" of The Principles of Quantum Mechanics by P. A. M. Dirac
In the development of the quantum theory, two different formulations have been given, one by Heisenberg and the other by Schrödinger. These two formulations are connected with each other by a general principle of duality. Heisenberg's matrix mechanics is based on the use of matrices to represent physical quantities. In this formulation, the state of a system is described by a state vector, and the observables of the system are represented by matrices. The evolution of the system is governed by matrix equations, which give the time evolution of the state vector. On the other hand, Schrödinger's wave mechanics uses wave functions to describe the state of a system. In this formulation, the observables of the system are represented by differential operators, and the evolution of the system is governed by the Schrödinger equation. Despite the apparent differences between the two formulations, it has been shown that Heisenberg's matrix mechanics is equivalent to Schrödinger's wave mechanics. The equivalence between the two formulations is esta...
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