On a technique for finding eigenvalues of a one-dimensional time-independent Schrödinger equation

SHEELA ROZARIO and BERNARDINE R WONG

Research Report No. 2/2003

Abstract

We implement a technique to determine the eigenvalues for bound-states of a one-dimensional time-independent Schrödinger equation. Using an initial guess value for the eigenvalue, the logarithmic derivative of the wavefunction is propagated (instead of the wavefunction itself) towards a suitable intermediate point from the boundaries of the domain considered. This enables the calculation of a correction to the guessed eigenvalue. An iteration of the process leads to rapid convergence due to the use of the Newton-Raphson method. We also demonstrate that this method provides an alternative approach to analytically determine exact eigenvalues and eigenvectors in the case of an infinite square well potential.