Study of the singular anharmonic potentials by means of the analytic continuation method

Abstract

Abstract. Here we study the singular anharmonic potentials by applying the analytic continuation method of Holubec and Stauffer. In order to do that we have developed several approximations to the problem, because this method cannot be applied when the solution has essential singularities &any point of its domain. All the options here shown have the same precision, giving us the eigenvalues correct to all the decimal places provided by the computer.

Ground and excited states of spherically symmetric potentials through an imaginary-time evolution method: application to spiked harmonic oscillators

“…It is seen that the present methodology offers results which are in good agreement with these. The most accurate results are those from analytic continuation method [55] and generalized pseudospectral method [20]. The present energies are not superior to these, but still are excellent and evidently better than many other reference values.…”

“…In all cases, the present eigenvalues match excellently with these. However they do not reach the accuracy reported in the references [20,55]. No references are available for higher states and we present here to illustrate the performance of current approach for = 0 situations.…”

“…Also, in the region of α ≥ 5/2, it exhibits super-singularity. For many other facets of this potential, the reader is referred to the following references [20,[54][55][56][57][58][59][60][61][62], Both the α values considered can lead to super-singularity; these have been studied by numerous analytic, semi-analytic as well as numerical methodologies. Some of these literature results are given here for comparison.…”

“…Reference[55] b Reference[20] c Reference[54] d Reference[56] e Reference[57] f Reference[58] g Reference[59] h Reference[60] …”

Quasilinearization approach to computations with singular potentials

“…Their results with accuracy of 20 significant figures are given in Table 1 together with the results of previous, less precise calculations, made using a method of one parameter coordinate transformation suggested by Killingbeck et al [34] To be sure that λ = 0.0001 is not accidentally a special case of small λ and that other small values of λ can also be computed Table 1 Ground state energies for λ = 0.0001 and different powers α. All Table 2 together with the value obtained with the help of the analytic continuation method by Buendía et al [35].…”