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Applied Spectroscopy

Applied Spectroscopy


  • Vol. 24, Iss. 1 — Jan. 1, 1970
  • pp: 73–80

Eigenvalues of the Potential Function V=z4±Bz2 and the Effect of Sixth Power Terms

Jaan Laane

Applied Spectroscopy, Vol. 24, Issue 1, pp. 73-80 (1970)

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The one-dimensional Schrödinger equation in reduced form is solved for the potential function V=z4+Bz2 where B may be positive or negative. The first 17 eigenvalues are reported for 58 values of B in the range −50 ≤ B ≤ 100. The interval of B between the tabulated values is sufficiently small so that the eigenvalues for any B in this range can be found by interpolation. At the limits of the range of B the potential function approaches that of a harmonic oscillator with only small anharmonicity. The effect of a small Cz6 term on this potential is studied and it is concluded that a previously reported approximation formula is quite applicable but only for positive values of B. The success of the quartic–harmonic potential function for the analysis of the ring-puckering vibration is shown; it is also demonstrated that the same potential serves as a useful approximation for many other systems, especially those of the double minimum type.

Jaan Laane, "Eigenvalues of the Potential Function V=z4±Bz2 and the Effect of Sixth Power Terms," Appl. Spectrosc. 24, 73-80 (1970)

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