TY - JOUR

T1 - Quantization in molecular potentials

AU - Trost, J.

AU - Eltschka, C.

AU - Friedrich, H.

PY - 1998/2/14

Y1 - 1998/2/14

N2 - We present a modified Bohr-Sommerfeld quantization rule for calculating energy levels in a molecular potential; it is based on the appropriate consideration of the reflection phase at the outer turning point. When the attractive tail of the potential is given by an inverse power law with a power greater than two, the reflection phase is accurately approximated by a simple algebraic formula. In an example defined by a 12-6 Lennard-Jones potential, this simple modified quantization rule gives highly accurate energy levels in the whole spectrum; the error relative to the level spacing is uniformly near 2 × 10-4. Very close to threshold, where the conventional WKB expansion breaks down completely, our simple formula can be supplemented by an accurate 'effective-range' expansion. This yields energies for the most weakly bound level with residual errors which are smaller than the level spacing to the second most weakly bound level by seven powers of ten.

AB - We present a modified Bohr-Sommerfeld quantization rule for calculating energy levels in a molecular potential; it is based on the appropriate consideration of the reflection phase at the outer turning point. When the attractive tail of the potential is given by an inverse power law with a power greater than two, the reflection phase is accurately approximated by a simple algebraic formula. In an example defined by a 12-6 Lennard-Jones potential, this simple modified quantization rule gives highly accurate energy levels in the whole spectrum; the error relative to the level spacing is uniformly near 2 × 10-4. Very close to threshold, where the conventional WKB expansion breaks down completely, our simple formula can be supplemented by an accurate 'effective-range' expansion. This yields energies for the most weakly bound level with residual errors which are smaller than the level spacing to the second most weakly bound level by seven powers of ten.

UR - http://www.scopus.com/inward/record.url?scp=0000629897&partnerID=8YFLogxK

U2 - 10.1088/0953-4075/31/3/006

DO - 10.1088/0953-4075/31/3/006

M3 - Article

AN - SCOPUS:0000629897

SN - 0953-4075

VL - 31

SP - 361

EP - 374

JO - Journal of Physics B: Atomic, Molecular and Optical Physics

JF - Journal of Physics B: Atomic, Molecular and Optical Physics

IS - 3

ER -