Quantization of the Liénard II equation and Jacobi’s last multiplier

Choudhury, A. Ghose; Guha, Partha

doi:10.1088/1751-8113/46/16/165202

Cited by 22 publications

(36 citation statements)

References 45 publications

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“…In this section we will be specifically concerned with the quantized version of (21) and seek a solution of the corresponding Schrödinger equation having momentum-dependent mass and the potential function given in (22) in contrast to the coordinate-dependent mass situation that has been well studied in the literature [15,16,17,18,19] in the configuration space. In fact taking cue from such investigations we begin this section with a von Roos type of decomposition [20] for the generic Hamiltonian in the momentum space…”

Section: The Schrödinger Equation With a Momentum Dependent Massmentioning

confidence: 99%

On quantized Liénard oscillator and momentum dependent mass

Bagchi

Choudhury²,

Guha

2015

Journal of Mathematical Physics

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We examine the analytical structure of the nonlinear Liénard oscillator and show that it is a bi-Hamiltonain system depending upon the choice of the coupling parameters. While one has been recently studied in the context of a quantized momentumdependent mass system, the other Hamiltonian also reflects a similar feature in the mass function and also depicts an isotonic character. We solve for such a Hamitonian and give the complete solution in terms of a confluent hypergeometric function.Mathematical Classification 70H03, 81Q05. *

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Section: The Schrödinger Equation With a Momentum Dependent Massmentioning

confidence: 99%

On quantized Liénard oscillator and momentum dependent mass

Bagchi

Choudhury²,

Guha

2015

Journal of Mathematical Physics

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“…Also, we have shown that if we replace the independent variable t with τ = it, then Equation (8) is transformed into Equation (20), which is one of the isochronous Liénard II equations [33]. Its corresponding Schrödinger equation was derived in [23,34]. The eigenfunctions and energy eigenvalues are given in (23) and (24), respectively.…”

Section: Discussion and Final Remarksmentioning

confidence: 99%

“…The quantization of Equation (21) was given in [34]. In [23], the quantization that preserves the Noether symmetries was applied to all equations (21).…”

Section: Quantizing With Noether Symmetriesmentioning

confidence: 99%

Noether Symmetries Quantization and Superintegrability of Biological Models

Nucci

Sanchini

2016

Symmetry

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It is shown that quantization and superintegrability are not concepts that are inherent to classical Physics alone. Indeed, one may quantize and also detect superintegrability of biological models by means of Noether symmetries. We exemplify the method by using a mathematical model that was proposed by Basener and Ross (2005), and that describes the dynamics of growth and sudden decrease in the population of Easter Island.

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“…Our strategy now is to deduce a constant mass Schrödinger equation from (19) in the new coordinate variable g corresponding to the potential U(g) with the same energy eigenvalue E of the PDM system (17). It can be achieved by choosing…”

Section: Quantum Solvability Of Hermitian Hamiltonianmentioning

confidence: 99%

“…Other classes of nonlinear oscillators have also been studied in the context of PDM problem [16][17][18] .…”

Section: Introductionmentioning

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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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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Quantization of the Liénard II equation and Jacobi’s last multiplier

Cited by 22 publications

References 45 publications

On quantized Liénard oscillator and momentum dependent mass

On quantized Liénard oscillator and momentum dependent mass

Noether Symmetries Quantization and Superintegrability of Biological Models

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

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