New kinetic energy operator for variable mass systems

Vubangsi, M.; Tchoffo, Martin; Fai, Lukong Cornelius

doi:10.1140/epjp/i2014-14105-4

Cited by 19 publications

(18 citation statements)

References 26 publications

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“…In the following section, we consider the Hermitian Hamiltonian of the form (11). We take up the case of non-Hermitian ordered Hamiltonian (3) in the succeeding section 4.…”

Section: Methods (Ii) Similarity Transformationmentioning

confidence: 99%

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Removal of ordering ambiguity for a class of position dependent mass quantum systems with an application to the quadratic Liénard type nonlinear oscillators

Ruby

Chandrasekar

Senthilvelan

et al. 2015

Journal of Mathematical Physics

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We consider the problem of removal of ordering ambiguity in position dependent mass quantum systems characterized by a generalized position dependent mass Hamiltonian which generalizes a number of Hermitian as well as non-Hermitian ordered forms of the Hamiltonian. We implement point canonical transformation method to map one-dimensional time-independent position dependent mass Schrödinger equation endowed with potentials onto constant mass counterparts which are considered to be exactly solvable. We observe that a class of mass functions and the corresponding potentials give rise to solutions that do not depend on any particular ordering, leading to the removal of ambiguity in it. In this case, it is imperative that the ordering is Hermitian.For non-Hermitian ordering we show that the class of systems can also be exactly solvable and are also shown to be iso-spectral using suitable similarity transformations. We also discuss the normalization of the eigenfunctions obtained from both Hermitian and non-Hermitian orderings.We illustrate the technique with the quadratic Liénard type nonlinear oscillators, which admit position dependent mass Hamiltonians.

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“…In the following section, we consider the Hermitian Hamiltonian of the form (11). We take up the case of non-Hermitian ordered Hamiltonian (3) in the succeeding section 4.…”

Section: Methods (Ii) Similarity Transformationmentioning

confidence: 99%

“…In the literature, the kinetic energy operatorT , which consists of position-dependent mass m(x) and momentump, is expressed in numerous ways in different situations 10,11 . We point out a few: …”

Section: Ordering Ambiguitymentioning

confidence: 99%

Removal of ordering ambiguity for a class of position dependent mass quantum systems with an application to the quadratic Liénard type nonlinear oscillators

Ruby

Chandrasekar

Senthilvelan

et al. 2015

Journal of Mathematical Physics

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“…It is important to note that the first term in the right-hand side of this expression is the same as the kinetic term in effective Hamiltonian (10). This allows us to write effective Hamiltonian (10) as a sum of kinetic energy (19) and potential energy…”

Section: Different Types Of Orderingmentioning

confidence: 99%

“…The author made the calculation accurate to the second order in the gradient operator. Finishing this short review on ordering problem, we would like to cite recent paper [10] on this subject (see also references therein).…”

Section: Introductionmentioning

confidence: 99%

Effective Hamiltonian with position-dependent mass and ordering problem

Tkachuk

Voznyak

2015

Eur. Phys. J. Plus

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We derive the effective low energy Hamiltonian for the tight-binding model with the hopping integral slowly varying along the chain. The effective Hamiltonian contains the kinetic energy with position dependent mass, which is inverse to the hopping integral, and effective potential energy. Changing of ordering in the kinetic energy leads to change of the effective potential energy and leaves the Hamiltonian the same one. Therefore, we can choose arbitrary von Roos ordering parameters in the kinetic energy without changing the Hamiltonian. Moreover, we propose a more general form for the kinetic energy than that of von Roos, which nevertheless together with the effective potential energy represent the same Hamiltonian.

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“…We can mention among others: the approach of the displacement operator, the application of the Meijer G-functions for the analytical solutions, the transport and dispersion properties at heterojunctions, etc. [6]. This field of study has emerged in favor of the development of the fabrication of semiconductors with very small dimensions and remarkable quantum effects.…”

Section: Introductionmentioning

confidence: 99%

Supersymmetric approach to coherent states for nonlinear oscillator with spatially dependent effective mass

Tchoffo

Migueu

Vubangsi

et al. 2019

Heliyon

Self Cite

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A nonlinear oscillator with variable mass is studied in the approach of Supersymmetric quantum mechanics. Ladder operators in association with the shape invariance condition allowed us to find the coherent states of the system in the sense of Barut and Girardello. The statistical properties of these particular states are studied using the probability of distribution. In addition, the vibrational partition function is calculated. We see that the thermodynamic functions of the system such as mean energy and entropy depend on the nonlinearity parameter, except for the specific heat.

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New kinetic energy operator for variable mass systems

Abstract: The Dirac kinetic energy form of the normal mass shift is widely used in relativistic atomic structure calculations. In the present paper, we illustrate the progressive breakdown of this operator with the increase of the nuclear charge along the lithium isoelectronic series.

Cited by 19 publications

References 26 publications

Removal of ordering ambiguity for a class of position dependent mass quantum systems with an application to the quadratic Liénard type nonlinear oscillators

Removal of ordering ambiguity for a class of position dependent mass quantum systems with an application to the quadratic Liénard type nonlinear oscillators

Effective Hamiltonian with position-dependent mass and ordering problem

Supersymmetric approach to coherent states for nonlinear oscillator with spatially dependent effective mass

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