Approximations to the eigenvalues of the Hamiltonian P<sup>2</sup>+A mod X<sup>nu </sup> mod in the Weyl correspondence limit-a critical appraisal of Turschner's formula
B J B Crowley; T F Hill; B J B Crowley; Dept. of Theoretical Phys., Univ. of Oxford, Oxford, UK; T F Hill; Dept. of Theoretical Phys., Univ. of Oxford, Oxford, UK
Журнал:
Journal of Physics A: Mathematical and General
Дата:
1979-09-01
Аннотация:
Accurate numerical calculations performed for the linear, quartic and square-well potentials (V(X)=A mod X<sup>nu </sup> 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)=P<sup>2</sup>+A mod X<sup>nu </sup> 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.
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