A remarkable property of a large class of functions is exploited to generate exact solutions to the one-dimensional Schrodinger equation. The method is simple and easy to implement.

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Simple exact solution of the one-dimensional Schrödinger equation with continuous plus δ -function potentials of arbitrary position and strength

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American Journal of Physics

Computer Solutions to Some Simple One-Dimensional Schrödinger Equations

John R. Merrill, Gregory P. Hughes

Published Nov 1, 1971• 3 citations

Publisher

DOI: 10.1119/1.1976666

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A simple exact solution of a one-dimensional Schr\"odinger equation which describes the motion of a particle in a continuous potential $V(x)$ and scattering from a finite set of $\ensuremath{\delta}$-function potentials of arbitrary positions and strengths is found.A simple exact solution of a one-dimensional Schr\"odinger equation which describes the motion of a particle in a continuous potential $V(x)$ and scattering from a finite set of $\ensuremath{\delta}$-function potentials of arbitrary positions and strengths is found.

Physical Review AAug 1, 19804 citations

A simple exact solution of a one-dimensional Schr\"odinger equation which describes the motion of a particle in a continuous potential

V(x)

and scattering from a finite set of $\ensuremath{\delta}$-function potentials of arbitrary positions and strengths is found.