Generalized space and linear momentum operators in quantum mechanics

Costa, Bruno G. da; Borges, Ernesto P.

doi:10.1063/1.4884299

Cited by 42 publications

(41 citation statements)

References 26 publications

(29 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We consider that the techniques employed in this work could stimulate the seek of other generalizations of classical and quantum mechanical aspects, as has been reported in recent research studies by means of the q-algebra. 7,[48][49][50][51][52][53][54][55][56]…”

Section: Discussionmentioning

confidence: 99%

“…Complementarily, it has been found that the mathematical foundations of the PDM systems rely on the assumption of the noncommutativity between the mass operator m(x) and the linear momentum operatorp, thus giving place to the ordering problem for the kinetic energy operator. 4,[40][41][42][43][44][45][46][47] In addition, the development of generalized translation operators motivated the introduction of a positiondependent linear momentum for characterizing a particle with a PDM 7,[48][49][50][51][52][53][54][55][56] that can be related to a generalized algebraic structure (called q-algebra 57 ) inherited from the mathematical background of nonextensive statistics. 58 Concerning these formal structures, the κ-deformed statistics, originated from the κ-exponential and κ-logarithm functions, allows us to develop an algebraic structure, called κ-algebra, [59][60][61][62][63][64][65][66][67][68][69][70][71][72][73][74] with similar properties to those of the q-algebra.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

κ-Deformed quantum and classical mechanics for a system with position-dependent effective mass

Costa

Gomez

Portesi

2020

Journal of Mathematical Physics

Self Cite

View full text Add to dashboard Cite

We present the quantum and classical mechanics formalisms for a particle with a position-dependent mass in the context of a deformed algebraic structure (named κ-algebra), motivated by the Kappa-statistics. From this structure, we obtain deformed versions of the position and momentum operators, which allow us to define a point canonical transformation that maps a particle with a constant mass in a deformed space into a particle with a position-dependent mass in the standard space. We illustrate the formalism with a particle confined in an infinite potential well and the Mathews-Lakshmanan oscillator, exhibiting uncertainty relations depending on the deformation.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

κ-Deformed quantum and classical mechanics for a system with position-dependent effective mass

Costa

Gomez

Portesi

2020

Journal of Mathematical Physics

Self Cite

View full text Add to dashboard Cite

show abstract

“…= e z ) (and its associated q-Gaussian [78]) has already emerged in a considerable amount of nonextensive and similar systems (see [6,38,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104] among others), as the appropriate generalization of the exponential one (and its associated Gaussian) (with regard to the nonlinear quantum equations introduced in [103], see also [105,106,107,108,109,110,111,112,113,114,115]). Therefore, it appears as rather natural to conjecture that, in some sense that remains to be precisely defined, the LDT expression e −r 1 N becomes generalized into something close to e −rqN q (q ∈ R), where the generalized rate function r q should be some generalized entropic quantity per particle.…”

Section: Towards a Generalized Large-deviation Theorymentioning

confidence: 99%

Inter-occurrence times and universal laws in finance, earthquakes and genomes

Tsallis

2016

Chaos, Solitons & Fractals

View full text Add to dashboard Cite

A plethora of natural, artificial and social systems exist which do not belong to the Boltzmann-Gibbs (BG) statistical-mechanical world, based on the standard additive entropy S BG and its associated exponential BG factor. Frequent behaviors in such complex systems have been shown to be closely related to q-statistics instead, based on the nonadditive entropy S q (with S 1 = S BG ), and its associated q-exponential factor which generalizes the usual BG one. In fact, a wide range of phenomena of quite different nature exist which can be described and, in the simplest cases, understood through analytic (and explicit) functions and probability distributions which exhibit some universal features. Universality classes are concomitantly observed which can be characterized through indices such as q. We will exhibit here some such cases, namely concerning the distribution of inter-occurrence (or interevent) times in the areas of finance, earthquakes and genomes.

show abstract

“…Electric mass ' ' and magnetic mass 2 can be thought of as two quantum states. The quantum operator [9,10] for mass can be written as…”

Section: Initial Concepts Of the New Theorymentioning

confidence: 99%

An Approach to Quantum Gravitodynamics and Some Important Results

Chakravorti¹,

Islam²,

Faruque³

2020

WJAP

View full text Add to dashboard Cite

We present in this article a new approach to the theory of gravitation. Here, the gravitational field of a gravitating body is assumed to be four fold. The gravitating body of mass M possesses gravitoelectric mass M, gravitomagnetic mass -2M. The test particle possess electric and magnetic masses that are algebraically of the same sign of that of the source body, i.e., m and -2m. Based on the electrostatic force formula, we find four forces acting on the test particle. The sum of these forces gives exactly the Newtonian gravitation force and gravitational potential energy. The classical theory of this approach yields four sets of Maxwellian equations and thus, four spin 1 bosons convey the complete force of gravity. The quantum version of this approach to gravity is illustrated here by presenting the fundamental Feynman diagrams that issue from the new theory. We work out scattering cross-section of interaction of an electron with a fixed gravitating mass partially. Of the four Feynman diagrams, we work out cross-section of scattering for only the simplest diagram. The non-relativistic limit of the cross-section is found and compared with that of electric Rutherford scattering. It is found that the electromagnetic cross-section is 10 17 times larger than the gravitational cross-section for the one process we considered. The work is fundamental and sheds new light onto quantum gravitodynamics.

show abstract

Generalized space and linear momentum operators in quantum mechanics

Cited by 42 publications

References 26 publications

κ-Deformed quantum and classical mechanics for a system with position-dependent effective mass

κ-Deformed quantum and classical mechanics for a system with position-dependent effective mass

Inter-occurrence times and universal laws in finance, earthquakes and genomes

An Approach to Quantum Gravitodynamics and Some Important Results

Contact Info

Product

Resources

About