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Physical Review

A Solution of the Schrödinger Equation by a Perturbation of the Boundary Conditions

H. Froehlich

Published Dec 1, 1938• 35 citations
Publisher

Abstract

A perturbation method is developed which allows a simple calculation of the eigenvalues of the Schrödinger equation by a slight change in the boundary condition.Received 29 September 1938DOI:https://doi.org/10.1103/PhysRev.54.945©1938 American Physical Society

DOI
10.1103/physrev.54.945

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A perturbation method is developed which allows a simple calculation of the eigenvalues of the Schrödinger equation by a slight change in the boundary condition.Received 29 September 1938DOI:https://doi.org/10.1103/PhysRev.54.945©1938 American Physical Society
Abstract Supplements on perturbation theory Change of boundary conditions Some problems in quantum mechanics can be approximated by a motion of a particle conflned in a definite region of space, bounded by certain surface, S0(x) = 0 In the case of Schro¨dinger’s equation a typical eigenvalue problem is of the form,: Supposing that we know how to solve the problem (21.1), what about the problem in which the boundary is slightly changed, i.e., in which the boundary is now given by A possible strategy is to seek for a change of the variables such that i.e., such that in terms of the new variables the equation determining the boundary has the original form S0 and therefore with the same problem as the original one (whose solution is known).