Eigenvalues of the Potential Function V=z 4±Bz 2 and the Effect of Sixth Power Terms

$29.00 plus tax (Refund Policy)

Buy Article:


The one-dimensional Schrödinger equation in reduced form is solved for the potential function V=z 4+Bz 2 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 Cz 6 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.

Keywords: Computer applications; Far infrared; Inversion, internal rotation, and double minimum type vibrations; Potential functions for ring-puckering

Document Type: Research Article

DOI: http://dx.doi.org/10.1366/000370270774372047

Affiliations: Department of Chemistry, Texas A&M University, College Station, Texas 77843

Publication date: January 1, 1970

More about this publication?
Related content



Share Content

Access Key

Free Content
Free content
New Content
New content
Open Access Content
Open access content
Subscribed Content
Subscribed content
Free Trial Content
Free trial content
Cookie Policy
Cookie Policy
ingentaconnect website makes use of cookies so as to keep track of data that you have filled in. I am Happy with this Find out more