Provider: ingentaconnect
Database: ingentaconnect
Content: application/x-research-info-systems
TY - ABST
AU - Laane, Jaan
TI - Eigenvalues of the Potential Function *V=z*
^{4}±*Bz*
^{2} and the Effect of Sixth Power Terms
JO - Applied Spectroscopy
PY - 1970-01-01T00:00:00///
VL - 24
IS - 1
SP - 73
EP - 80
KW - Potential functions for ring-puckering
KW - Inversion, internal rotation, and double minimum type vibrations
KW - Far infrared
KW - Computer applications
N2 - 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.
UR - http://www.ingentaconnect.com/content/sas/sas/1970/00000024/00000001/art00014
M3 - doi:10.1366/000370270774372047
UR - http://dx.doi.org/10.1366/000370270774372047
ER -