Generalization of quasi-exactly solvable and isospectral potentials

Bera, Pulakesh; Datta, Jayita; Panja, M. M.; Sil, Tapas

doi:10.1007/s12043-007-0137-y

Cited by 3 publications

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“…AHOs also serve as a test bench for different approximate methods of getting solutions of Schrödinger equation and to examine the ability of an approximation method to reproduce the dependence of the eigenvalues on the coefficients of the potential [12]. Most of the AHOs belongs to the family of quasi-exactly solvable potentials for which the exact energy eigenvalues and eigenfunctions can be obtained for a few low lying states [13,14,15,16,17]. Attempts are going on for getting solutions for higher states or for unrestricted values of the parameters admissible to the existence of bound states for such potentials [18,19,20,21].…”

Section: Introductionmentioning

confidence: 99%

Study of the sextic and decatic anharmonic oscillators using an interpolating scale function

et al. 2020

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Anharmonic oscillators with the sextic and decatic potentials are studied employing the refinable interpolating scale functions. This method yields highly accurate values of both energy eigenvalues and eigenfunctions for the sextic and decatic oscillator without constraining the potential parameters. Convergence of the solutions in the present method is noticed to be very fast. PACS. 0 3.65.Ge, 02.60.-x, 02.70.-c Send offprint requests to:

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Section: Introductionmentioning

confidence: 99%

Study of the sextic and decatic anharmonic oscillators using an interpolating scale function

et al. 2020

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Iterative approach for the eigenvalue problems

Datta

Bera²

2011

Pramana - J Phys

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An approximation method based on the iterative technique is developed within the framework of linear delta expansion (LDE) technique for the eigenvalues and eigenfunctions of the one-dimensional and three-dimensional realistic physical problems. This technique allows us to obtain the coefficient in the perturbation series for the eigenfunctions and the eigenvalues directly by knowing the eigenfunctions and the eigenvalues of the unperturbed problems in quantum mechanics. Examples are presented to support this. Hence, the LDE technique can be used for nonperturbative as well as perturbative systems to find approximate solutions of eigenvalue problems.Keywords. Formulation of iterative technique for one dimension and applications; formulation of iterative technique for three dimensions and applications.

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On some polynomial potentials in d-dimensions

Brandon

Saad

Dong

2013

Journal of Mathematical Physics

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The d-dimensional Schrödinger's equation is analyzed with regard to the existence of exact solutions for polynomial potentials. Under certain conditions on the interaction parameters, we show that the polynomial potentials $V_8(r) =\sum _{k=1}^8 \alpha _kr^k, \alpha _8>0$V8(r)=∑k=18αkrk,α8>0 and $V_{10}(r)= \sum _{k=1}^{10} \alpha _kr^k, \alpha _{10}>0$V10(r)=∑k=110αkrk,α10>0 are exactly solvable. By examining the polynomial solutions of certain linear differential equations with polynomial coefficients, the necessary and sufficient conditions for the existence of these exact solutions are discussed. Finding accurate solutions for arbitrary values of the potential parameters using the asymptotic iteration method is also presented.

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Generalization of quasi-exactly solvable and isospectral potentials

Abstract: A unified approach in the light of supersymmetric quantum mechanics (SSQM) has been suggested for generating multidimensional quasi-exactly solvable (QES) potentials. This method provides a convenient means to construct isospectral potentials of derived potentials.

Cited by 3 publications

References 30 publications

Study of the sextic and decatic anharmonic oscillators using an interpolating scale function

Study of the sextic and decatic anharmonic oscillators using an interpolating scale function

Iterative approach for the eigenvalue problems

On some polynomial potentials in d-dimensions

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