Displacement operator for quantum systems with position-dependent mass

Filho, R. N. Costa; Almeida, Murilo P.; Farias, G. A.; Andrade, José S.

doi:10.1103/physreva.84.050102

Cited by 107 publications

(138 citation statements)

References 24 publications

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“…[1], which is summarised here. Costa Filho et al introduced a characteristic inverse length scale, γ, in the translation operator defined by [1]:…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…Depending on the value of γ, position space is either contracted or dilated, and was shown to affect the energy spectrum and probability amplitude of a free-particle and an infinitely confined particle, respectively [1]. Eq.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…The introduction of a spatially dependent effective mass (SPDEM) in the Hamiltonian has benefited research from quantum gravity to condensed matter [1,2]. In semiconductor physics, a SPDEM can be applied to doped semiconductors, or when there exists a graded potential [3][4][5].…”

Section: Introductionmentioning

confidence: 99%

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Quantum confinement in nonadditive space with a spatially dependent effective mass for Si and Ge quantum wells

Barbagiovanni¹,

Filho²

2014

Physica E: Low-dimensional Systems and Nanostructures

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We calculate the effect of a spatially dependent effective mass (SPDEM) [adapted from R. N. Costa Filho et al.Phys. Rev. A., 84 050102 (2011)] on an electron and hole confined in a quantum well (QW). In the work of Costa Filho et al., the translation operator is modified to include an inverse character length scale, γ, which defines the SPDEM.The introduction of γ means translations are no longer additive. In nonadditive space, we choose a 'skewed' Gaussian confinement potential defined by the replacement x → γ −1 ln(1 + γx) in the usual Gaussian potential. Within the parabolic approximation γ is inversely related to the QW thickness and we obtain analytic solutions to our confinement Hamiltonian. Our calculation yields a reduced dispersion relation for the gap energy (E G ) as a function of QW thickness,Additionally, nonadditive space contracts the position space metric thus increasing the occupied momentum space and reducing the effective mass, in agreement the relation:The change in the effective mass is shown to be a function of the confinement potential via a point canonical transformation. Our calculation agrees with experimental measurements of E G for Si and Ge QWs.

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“…[1], which is summarised here. Costa Filho et al introduced a characteristic inverse length scale, γ, in the translation operator defined by [1]:…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Section: Theoretical Backgroundmentioning

confidence: 99%

See 1 more Smart Citation

Quantum confinement in nonadditive space with a spatially dependent effective mass for Si and Ge quantum wells

Barbagiovanni¹,

Filho²

2014

Physica E: Low-dimensional Systems and Nanostructures

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“…The nonadditive characteristic of S q [8,9,10] has also brought new insights to several works in the area of complex systems [9,10] and contributed to diverse problems of quantum mechanics [11,12,13,14,15,16,17,18,19,20,21]. Recently, Nobre, Rego-Monteiro and…”

Section: Introductionmentioning

confidence: 99%

Solutions for a q-generalized Schrödinger equation of entangled interacting particles

Alves

Ribeiro

Santos

et al. 2015

Physica A: Statistical Mechanics and its Applications

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We report on the time dependent solutions of the q−generalized Schrödinger equation proposed by Nobre et al. [Phys. Rev. Lett. 106, 140601 (2011)]. Here we investigate the case of two free particles and also the case where two particles were subjected to a Moshinsky-like potential with time dependent coefficients. We work out analytical and numerical solutions for different values of the parameter q and also show that the usual Schrödinger equation is recovered in the limit of q → 1. An intriguing behavior was observed for q = 2, where the wave function displays a ring-like shape, indicating a bind behavior of the particles.Differently from the results previously reported for the case of one particle, frozen states appear only for special combinations of the wave function parameters in case of q = 3. Highlights Solutions of a nonlinear Schrödinger equation;Time dependent wave functions;Free particles and Moshinsky-like potential.

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“…Displacement operators have already been introduced for systems with position-dependent-mass, for null or constant potentials from which generalized forms of the momentum operator have been obtained [26,27].…”

Section: Introductionmentioning

confidence: 99%

A squeeze-like operator approach to position-dependent mass in quantum mechanics

Moya‐Cessa

Soto‐Eguibar

Christodoulides

2014

Journal of Mathematical Physics

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Displacement operator for quantum systems with position-dependent mass

Cited by 107 publications

References 24 publications

Quantum confinement in nonadditive space with a spatially dependent effective mass for Si and Ge quantum wells

Quantum confinement in nonadditive space with a spatially dependent effective mass for Si and Ge quantum wells

Solutions for a q-generalized Schrödinger equation of entangled interacting particles

A squeeze-like operator approach to position-dependent mass in quantum mechanics

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