Ground-state energy eigenvalue calculation of the quantum mechanical well $V(x)=1/2k{x}^2+\lambda x^4$ via analytical transfer matrix method

Abstract

The analytical transfer matrix technique is applied to the Schrödinger equation of symmetric quartic-well potential problem in the form $V(x)=1/2k{x}^2+\lambda x^4.$ This gives quantization condition from which we can calculate the ground-state energy eigenvalues numerically. We also compare the results with those obtained from numerical shooting method, perturbation theory, and WKB method.

9 pages, 4 figures, IoP format

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