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

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

2007-11-09

arxiv.org/abs/0711.1469v1

Physics

Condensed Matter

Other Condensed Matter

9 pages, 4 figures, IoP format

Scientific paper

10.1088/0143-0807/29/3/017

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

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