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Physical Review A

Exact analytic solution of the Schrödinger equation with centrifugal tensor forces

J. Besprosvany, M. Moshińsky

Published Jun 1, 1998• 0 citations
Publisher

Abstract

We find the solution of the Schr"odinger equation for the case of a central square well (or barrier) plus a centrifugal tensor well potential for a system of two spin one-half particles. The wave function is derived and from it a scattering amplitude is obtained explicitly.
DOI
10.1103/physreva.57.4401

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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)V(x)V(x) and scattering from a finite set of $\ensuremath{\delta}$-function potentials of arbitrary positions and strengths is found.
A simple procedure has been found for the general solution of the time-independent Schrödinger equation (SE) with the help of quantization of potential area in one dimension without making any approximation. Energy values are not dependent on wave functions. So, to find the energy values, it is enough to find the classic turning points of the potential function. Two different solutions were obtained, namely, symmetric and antisymmetric in bound states. These normalized wave functions are always periodic. It is enough to take the integral of the square root of the potential energy function to find the normalized wave functions. If these calculations cannot be made analytically, they should then be performed by numerical methods. The SE has been solved for a particle in many one-dimension and the spherical symmetric central potential wells as examples. Their energies and normalized wave functions were found as examples. These solutions were also applied to the theories of scattering and alpha decay. The results obtained with the experimental values were compared with the calculated values. One was seen to be very fit.