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Approximations to the eigenvalues of the Hamiltonian P 2 +A mod X nu mod in the Weyl correspondence limit-a critical appraisal of Turschner's formula

1979; Institute of Physics; Volume: 12; Issue: 9 Linguagem: Inglês

10.1088/0305-4470/12/9/001

1361-6447

B.J.B. Crowley, T. F. Hill,

Quantum chaos and dynamical systems

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.