Approximations to the eigenvalues of the Hamiltonian P2+A mod Xnumod in the Weyl correspondence limit-a critical appraisal of Turschner's formula
- 1 September 1979
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 12 (9) , L223-L228
- https://doi.org/10.1088/0305-4470/12/9/001
Abstract
Accurate numerical calculations performed for the linear, quartic and square-well potentials (V(X)=A mod Xnu mod , nu =1,4, infinity ) fail to confirm the recent claim by Turschner to have found an exact closed-form formula for the eigenvalues of the Hamiltonian H(P,X)=P2+A mod Xnu mod for any nu >0. The formula is found to be an approximation (except for nu =2). However, for the lowest eigenvalues of the potentials considered, it is found to be significantly more accurate than the simple WKB approximation based upon the Bohr-Sommerfeld integral.Keywords
This publication has 3 references indexed in Scilit:
- Exact eigenvalues of the Hamiltonian P2+A mod X modnuJournal of Physics A: General Physics, 1979
- Discrepancies from Asymptotic Series and Their Relation to Complex Classical TrajectoriesPhysical Review Letters, 1978
- Ordered Expansions in Boson Amplitude OperatorsPhysical Review B, 1969