SUSY method for the three-dimensional Schrödinger equation with effective mass

Ioffe, M. V.; Kolevatova, E.V.; Nishnianidze, D. N.

doi:10.1016/j.physleta.2016.08.014

Cited by 17 publications

(8 citation statements)

References 79 publications

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“…We believe that the presented results can be treated as a challenge to generalize various branches of SUSY to the case of matrix superpotentials and position dependent masses. And it is nice that some elements of such generalizations can be already recognized in literature, see, e.g., [60,61,62,63,64,65].…”

Section: Discussionmentioning

confidence: 99%

Symmetries and Supersymmetries of Generalized Schrödinger equations

Nikitin

2020

Preprint

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Section: Discussionmentioning

confidence: 99%

Symmetries and Supersymmetries of Generalized Schrödinger equations

Nikitin

2020

Preprint

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“…Now one can utilize the constructed time-independent hamiltonain K to construct the wave functions in transformed space by methods like SUSY formalism [47][48][49][50][51][52]. By inverse transformation the wave functions in original space can be easily obtained.…”

Section: Canonical Transformationmentioning

confidence: 99%

Constraints on the choice of position dependent effective mass and external potential for the existence of Lewis-Riesenfeld invariance and quantum canonical transformation

Biswas,

Saha,

Patra

2020

Preprint

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Lewis-Riesenfeld -Ermakov's (LR) invariant method for the construction of time-dependent phase-space invariant is extended for the general quantum system with position-dependent effective mass (PDEM) Hamiltonian. It turns out that, only a specific class of PDEM and a particular class of external potentials will exhibit the LR-invariant operator in close form. Then we have determine a class of unitary time-dependent quantum canonical transformation for the concerned PDEM and external potentials so that an equivalent time-independent PDEM Hamiltonian is obtained.

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“…where n 1 , n 2 are two integer non-negative numbers, and according to (36), the variables x 1 = 2 √ ρ cos (ϕ/2); x 2 = 2 √ ρ sin (ϕ/2) are expressed in terms of the polar coordinates ρ, ϕ on the plane y. Using the properties of Hermite polynomials, it is not difficult to check that although a part of these solutions (when both n 1 and n 2 are even) is singular at the origin, all wave functions (39) are normalizable on the plane y.…”

Section: Examplesmentioning

confidence: 99%