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

Artit Hutem; Chanun Sricheewin

doi:10.1088/0143-0807/29/3/017

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arXiv · 0711.1469

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

Artit Hutem·Chanun Sricheewin

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Abstract

The analytical transfer matrix technique is applied to the Schrödinger equation of symmetric quartic-well potential problem in the form $V(x)={1/2}kx^{2}+λ{x^{4}}.$ 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.

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Artit Hutem, Chanun Sricheewin. 2007-11-09. Ground-state energy eigenvalue calculation of the quantum mechanical well $V(x)={1/2}kx^{2}+λ{x^{4}}$ via analytical transfer matrix method. https://doi.org/10.1088/0143-0807%2F29%2F3%2F017

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