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Solution of Schrödinger equation by Laplace transform

Published online by Cambridge University Press:  09 April 2009

M. J. Englefield
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Laplace transform techniques for solving differential equations do not seem to have been directly applied to the Schrödinger equation in quantum mechanics. This may be because the Laplace transform of a wave function, in contrast to the Fourier transform, has no direct physical significance. However, this paper will show that scattering phase shifts and bound state energies can be determined from the singularities of the Laplace transform of the wave function. The Laplace transform method can thereby simplify calculations if the potential allows a straightforward solution of the transformed Schrödinger equation. Suitable cases are the Coulomb, oscillator and exponential potentials and the Yamaguchi separable non-local potential.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 8 , Issue 3 , August 1968 , pp. 557 - 567
Copyright
Copyright © Australian Mathematical Society 1968

References

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