Oscillators with quartic anharmonicity: Approximate energy levels

Donald G. Truhlar

doi:10.1016/0022-2852(71)90123-8

Oscillators with quartic anharmonicity: Approximate energy levels

Donald G. Truhlar

Chemistry (Twin Cities)

Research output: Contribution to journal › Article › peer-review

31 Scopus citations

Abstract

A variation-perturbation method is presented for obtaining approximate eigenvalues of quantum mechanical oscillators with the potential energy function V(x) = ax⁴ + cx². Numerical results show that solution of a cubic equation can often yield energy differences between the levels accurate to better than 0.001%. The method is accurate for both high and low quantum numbers.

Original language	English (US)
Pages (from-to)	415-421
Number of pages	7
Journal	Journal of molecular spectroscopy
Volume	38
Issue number	2
DOIs	https://doi.org/10.1016/0022-2852(71)90123-8
State	Published - May 1971

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title = "Oscillators with quartic anharmonicity: Approximate energy levels",

abstract = "A variation-perturbation method is presented for obtaining approximate eigenvalues of quantum mechanical oscillators with the potential energy function V(x) = ax4 + cx2. Numerical results show that solution of a cubic equation can often yield energy differences between the levels accurate to better than 0.001\%. The method is accurate for both high and low quantum numbers.",

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N2 - A variation-perturbation method is presented for obtaining approximate eigenvalues of quantum mechanical oscillators with the potential energy function V(x) = ax4 + cx2. Numerical results show that solution of a cubic equation can often yield energy differences between the levels accurate to better than 0.001%. The method is accurate for both high and low quantum numbers.

AB - A variation-perturbation method is presented for obtaining approximate eigenvalues of quantum mechanical oscillators with the potential energy function V(x) = ax4 + cx2. Numerical results show that solution of a cubic equation can often yield energy differences between the levels accurate to better than 0.001%. The method is accurate for both high and low quantum numbers.

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U2 - 10.1016/0022-2852(71)90123-8

DO - 10.1016/0022-2852(71)90123-8

M3 - Article

AN - SCOPUS:37949047688

SN - 0022-2852

VL - 38

SP - 415

EP - 421

JO - Journal of molecular spectroscopy

JF - Journal of molecular spectroscopy

IS - 2

ER -

Oscillators with quartic anharmonicity: Approximate energy levels

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