Exact analytic solution of position-dependent mass Schrödinger equation

Rajbongshi, H.

doi:10.1007/s12648-017-1108-x

Cited by 9 publications

(4 citation statements)

References 46 publications

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“…Among them, Gauss hypergeometric and Bessel functions related to hyperbolic, exponential or rational functions have been found -see eqs. ( 17), ( 31), ( 43) and (50). In Table 4 we summarize the type of energy spectra of the whole diversity of arrangements.…”

Section: Final Discussionmentioning

confidence: 99%

“…Some experimental fits with BDD mass parameters can be also found in [39,57]. Notwithstanding, the other orderings have been adopted with success in some systems [50], particularly when interfaces are not brusque. For example, in the case of exponential modeling of potential and mass within a material, the BDD ordering is the one to be discarded [58].…”

Section: Introductionmentioning

confidence: 97%

“…We will apply point canonical transformations, which keep invariant the canonical form of the wave equation [11,21,22,42,43], but there exist alternative procedures like super-symmetric quantum mechanics [44][45][46], Lie algebras [47] and Weyl integral quantization [48,49] (more refs. in [23,50]), which have been also used in the last years.…”

Section: Introductionmentioning

confidence: 99%

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The kinetic Hamiltonian with position-dependent mass

Lima,

Christiansen

2023

Preprint

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In the present paper we examine in a systematic way the most relevant orderings of pure kinetic Hamiltonians for five different position-dependent mass (PDM) profiles: soliton-like, reciprocal quadratic and biquadratic, exponential and parabolic. As a result of the non-commutativity between momentum and position operators, a diversity of effective potentials is generated. We analyse the whole set and find unexpected coincidences as well as discrepancies among them. We obtain analytically the full-spectrum of energies and solutions in the twenty-five cases considered.It is shown how the simple ordinary constant-mass solutions are transformed into a variety of complex combinations of transcendental functions and arguments. We find that particles with a non-uniform mass density can present discrete energy spectra as well as continuous ones which can be bounded or not. These results are consistent with the fact that although the external potential is zero, PDM eigenfunctions are not actual free states but a sort of effective waves in a solid-state sample. This is precisely the origin of the position-dependent mass. In all the events we obtain exact complete spectral expressions. Our methodological procedure thus puts a wide diversity of Hamiltonian seeds on an equal footing in order to be compared. This allows choosing the better arrangement to model a specific solid or heterostructure once the spectrum of a given material is experimentally available. Finally, we perform a one-dimensional model calculation of a double heterostructure with a parabolic PDM particle in the interface region. Our study is also indicated for applications inside material structures with the addition of external potentials.

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Section: Final Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

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The kinetic Hamiltonian with position-dependent mass

Lima,

Christiansen

2023

Preprint

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“…While the interest in searching exactly solvable quantum PDM systems is still increasing [25,36], the most interesting question remains how to order the mass operator with respect to the momentum operator when it comes to building the KEO of the Hamiltonian. The dilemma does not seem obvious when the mass is constant, but when this latter becomes a function of the particle position, the bewilderment appears in the non-commutativity between the mass and the momentum operators.…”

Section: Introductionmentioning

confidence: 99%

A New Class of Exactly Solvable Models within the Schr&#246;dinger Equation with Position Dependent Mass

Dhahbi¹,

Chargui²,

Trablesi³

2019

JAMP

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Supersymmetric approach to approximate analytical solutions of the Klein-Gordon equation: application to a position-dependent mass and a hyperbolic cotangent vector potential

Zaghou,

Benamira

2023

Indian J Phys

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Exact analytic solution of position-dependent mass Schrödinger equation

Cited by 9 publications

References 46 publications

The kinetic Hamiltonian with position-dependent mass

The kinetic Hamiltonian with position-dependent mass

A New Class of Exactly Solvable Models within the Schr&#246;dinger Equation with Position Dependent Mass

Supersymmetric approach to approximate analytical solutions of the Klein-Gordon equation: application to a position-dependent mass and a hyperbolic cotangent vector potential

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Exact analytic solution of position-dependent mass Schrödinger equation

Cited by 9 publications

References 46 publications

The kinetic Hamiltonian with position-dependent mass

The kinetic Hamiltonian with position-dependent mass

A New Class of Exactly Solvable Models within the Schr&amp;#246;dinger Equation with Position Dependent Mass

Supersymmetric approach to approximate analytical solutions of the Klein-Gordon equation: application to a position-dependent mass and a hyperbolic cotangent vector potential

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A New Class of Exactly Solvable Models within the Schrödinger Equation with Position Dependent Mass