Harmonic oscillator with minimal length uncertainty relations and ladder operators

Dadic, I.; Jonke, Larisa; Meljanac, Stjepan

doi:10.1103/physrevd.67.087701

Cited by 89 publications

(90 citation statements)

References 26 publications

(34 reference statements)

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“…This assumption is not unjustifiable in view of the fact that the standard model charges cannot move in extra dimensions in theory of brane world model. Now, extra dimensions are widely accepted by theorists and there are large works about it [7][8][9][10][11][12][13]. This model gives us the new spectra, which looks same as our previous works [6], however, have different physical meaning.…”

Section: Introductionsupporting

confidence: 56%

Spectra of Hydrogen Atom with GUP and Extra Dimensions

Mu¹

2013

JMP

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We argue that the Generalized Uncertainty Ptinciple (GUP) and the compact Extra dimensions will lead the hydrogen atom has the non bounded state spectra which equal the free particle in extra dimensions. We use Generalized Uncertainty Principle (GUP) to calculate the new energy spectra of hydrogen atom, and which lives in three dimensional Euclidean spaces with one extra dimension. The result is not familiar with our known before that when n is large enough. In our modified new spectra, we obtain that, which is lager than zero.These new spectra give us new method to obtain the existence of extra dimensions. Finally, we find that the spectra are same as part of extra dimensions in planck scale.

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Section: Introductionsupporting

confidence: 56%

Spectra of Hydrogen Atom with GUP and Extra Dimensions

Mu¹

2013

JMP

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“…This is the reason why the sign of similarity appears in (22) and in the majority of subsequent relations. Later on, when we consider a construction of the bosonic ladder operators, we shall have to take care of the normalization of the wave functions and every single proportionality factor will be important.…”

Section: Bargmann Representation Analysismentioning

confidence: 99%

“…As was said previously, in order to find bosonic ladder operators [20][21][22] related to the eigenfunctions we were in search for, the knowledge on the detailed form of the normalization factor is essential. Thus, after we utilize the normalization properties of the Jacobi and Laguerre polynomials, we are left with the normalized version of the eigenfunctions (25) of the model Hamiltonian (1),…”

Section: Ladder Operatorsmentioning

confidence: 99%

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Quantization and conformal properties of a generalized Calogero model

et al. 2007

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We analyze a generalization of the quantum Calogero model with the underlying conformal symmetry, paying special attention to the two-body model deformation. Owing to the underlying SU (1, 1) symmetry, we find that the analytic solutions of this model can be described within the scope of the Bargmann representation analysis and we investigate its dynamical structure by constructing the corresponding Fock space realization. The analysis from the standpoint of supersymmetric quantum mechanics (SUSYQM), when applied to this problem, reveals that the model is also shape invariant. For a certain range of the system parameters, the two-body generalization of the Calogero model is shown to admit a one-parameter family of self-adjoint extensions, leading to inequivalent quantizations of the system. PACS number(s): 02.30. Ik, 03.65.Fd,

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“…Such approaches have been undergone and the analytical properties of the resulting theories have been investigated closely [15,16,17]. In the scenario without extra dimensions, the derived modifications are important mainly for structure formation and the early universe [18].…”

mentioning

confidence: 99%

The Minimal Length and Large Extra Dimensions

Hossenfelder

2004

Mod. Phys. Lett. A

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Planck scale physics represents a future challenge, located between particle physics and general relativity. The Planck scale marks a threshold beyond which the old description of spacetime breaks down and conceptually new phenomena must appear. Little is known about the fundamental theory valid at Planckian energies, except that it necessarily seems to imply the occurrence of a minimal length scale, providing a natural ultraviolet cutoff and a limit to the possible resolution of spacetime.Motivated by String Theory, the models of large extra dimensions lower the Planck scale to values soon accessible. These models predict a vast number of quantum gravity effects at the lowered Planck scale, among them the production of TeV-mass black holes and gravitons. Within the extra dimensional scenario, also the minimal length comes into the reach of experiment and sets a fundamental limit to short distance physics.We review the status of Planck scale physics in these effective models.

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Harmonic oscillator with minimal length uncertainty relations and ladder operators

Cited by 89 publications

References 26 publications

Spectra of Hydrogen Atom with GUP and Extra Dimensions

Spectra of Hydrogen Atom with GUP and Extra Dimensions

Quantization and conformal properties of a generalized Calogero model

The Minimal Length and Large Extra Dimensions

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