Quantum Mechanics on some Supermanifolds

Mezincescu, Luca

doi:10.1007/978-0-387-87499-9_13

Cited by 19 publications

(32 citation statements)

References 9 publications

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“…We briefly outline Bopp's shift method here; the details can be found in [47][48][49][50]. The physicist Fritz Bopp was the first to consider pseudodifferential operators obtained from a symbol by the quantization rules…”

Section: Revised the Md-(ihop And Ivqi) Models In Rqm Symmetriesmentioning

confidence: 99%

“…In the physics literature, this is known as Bopp's shift, and this quantization procedure is called Bopp quantization. It is known to the specialists that Bopp's shift method [47][48][49][50] has been applied effectively and has succeeded in simplifying the three basic equations deformed Schrödinger equation DSE [51][52][53][54][55][56][57][58][59][60][61][62], the DKGE [63][64][65][66][67][68][69][70][71][72][73][74], the deformed Dirac equation DDE [75][76][77][78][79][80] and the deformed Duffin-Kemmer equation [81][82][83][84] with the notion of star product to the SE, the KGE, the DE and the Duffin-Kemmer equation with the notion of ordinary product, respectively. The results of the application of this method were very useful and yielded promising results in many physical and chemical fields.…”

Section: Revised the Md-(ihop And Ivqi) Models In Rqm Symmetriesmentioning

confidence: 99%

“…The CNCCRs with star product in Eq. ( 2) become new CNCCRs without the notion of star product as follows (see, e.g., [47][48][49][50]):…”

Section: Revised the Md-(ihop And Ivqi) Models In Rqm Symmetriesmentioning

confidence: 99%

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The Effects of Noncommutativity on the Energy Spectra for Mass-Dependent Klein-Gordon and Shrödinger Equations with Vector Quark-Antiquark Interaction and Harmonic Oscillator Potential: Application to HLM Systems

2023

Bulg.J.Phys.

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The analytical solutions of the mass-dependent Klien-Gordon equation (KGE) with the improved harmonic oscillator potential and the improved vector quark-antiquark interaction are derived from the symmetries of threedimensional relativistic noncommutative quantum mechanics (3D-RNCQM symmetries) using Bopp's shift method and perturbation theory. The energy state equations are sensitive to the global parameters characterizing the noncommutativity space-space (Θ, σ) and the potential parameter (E nl , a,b, c, m0, k) in addition to the discrete atomic quantum numbers (j, l, s, m). The energy spectra for the mass-dependent Shrödinger equation with improved vector quarkantiquark interaction and harmonic oscillator potential were found using nonrelativistic limit principles. We also used the current findings to determine the heavy-meson masses of charmonium cc and bottomonium bb in both ordinary nonrelativistic quantum mechanics symmetries and three-dimensional nonrelativistic noncommutative 3D-NRNCQM symmetries.

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Section: Revised the Md-(ihop And Ivqi) Models In Rqm Symmetriesmentioning

confidence: 99%

Section: Revised the Md-(ihop And Ivqi) Models In Rqm Symmetriesmentioning

confidence: 99%

See 1 more Smart Citation

The Effects of Noncommutativity on the Energy Spectra for Mass-Dependent Klein-Gordon and Shrödinger Equations with Vector Quark-Antiquark Interaction and Harmonic Oscillator Potential: Application to HLM Systems

2023

Bulg.J.Phys.

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“…In order to express the Hamiltonian (Eqn. ( 1)) in commutative space we relate the NC coordinates (X i , P i ) to the commutative space variables (x i , p i ) by the standard Bopp-shift relations 7 which are mentioned below in natural unit = 1.…”

Section: Considering the Two-dimensional Harmonic Oscillator In The P...mentioning

confidence: 99%

Periodicity of damped harmonic oscillator affected by magnetic field in timedependent noncommutative space

2022

AJPSA

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A model of two-dimensional damped harmonic oscillator affected by time dependent magnetic field in time dependent noncommutative space was studied in an earlier communication [Phys. Scr. 96 (2021) 125224]. In this article, the same model is considered to show that, for a suitable explicit choices of damping and magnetic field, it is possible to import a periodicity to the time evolution of the energy expectation value of the model system.

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“…Dynamics depends on parameters θ and σ, what is more obvious from Hamiltonian (20) than relations (4). Consequently phase space transformations (6) are not (and should not be) canonical, because dynamics of our system is given not only by Hamiltonian (20) but with (20) and (4). In the case σ = 0, a similar result for Hamiltonian with parameter θ is obtained by the Moyal product procedure [6].…”

Section: ∂L ∂ẋAmentioning

confidence: 99%

Noncommutative classical and quantum mechanics for quadratic Lagrangians (Hamiltonians)

Драгович

Rakic

2009

Proc. Steklov Inst. Math.

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We consider classical and quantum mechanics for an extended Heisenberg algebra with additional canonical commutation relations for position and momentum coordinates. In our approach this additional noncommutativity is removed from the algebra by linear transformation of coordinates and transmitted to the Hamiltonian (Lagrangian). Since linear transformations do not change the quadratic form of Hamiltonian (Lagrangian), and Feynman's path integral has well-known exact expression for quadratic models, we restricted our analysis to this class of physical systems. The compact general formalism presented here can be easily realized in any particular quadratic case. As an important example of phenomenological interest, we explored model of a charged particle in the noncommutative plane with perpendicular magnetic field. We also introduced an effective Planck constant ef f which depends on noncommutativity.

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Quantum Mechanics on some Supermanifolds

Cited by 19 publications

References 9 publications

The Effects of Noncommutativity on the Energy Spectra for Mass-Dependent Klein-Gordon and Shrödinger Equations with Vector Quark-Antiquark Interaction and Harmonic Oscillator Potential: Application to HLM Systems

The Effects of Noncommutativity on the Energy Spectra for Mass-Dependent Klein-Gordon and Shrödinger Equations with Vector Quark-Antiquark Interaction and Harmonic Oscillator Potential: Application to HLM Systems

Periodicity of damped harmonic oscillator affected by magnetic field in timedependent noncommutative space

Noncommutative classical and quantum mechanics for quadratic Lagrangians (Hamiltonians)

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