Infinite wall in the fractional quantum mechanics

2021 ◽  
Vol 62 (3) ◽  
pp. 032104
Author(s):  
Jianping Dong ◽  
Ying Lu
Keyword(s):  
Quantum Mechanics ◽  
Fractional Quantum ◽  
Infinite Wall

scholarly journals Prospecting black hole thermodynamics with fractional quantum mechanics

2021 ◽  
Vol 81 (7) ◽  
Author(s):  
S. Jalalzadeh ◽  
F. Rodrigues da Silva ◽  
P. V. Moniz
Keyword(s):  
Black Hole ◽  
Quantum Mechanics ◽  
Main Tool ◽  
Acta Math ◽  
Black Hole Thermodynamics ◽  
Point Of View ◽  
Black Hole Mass ◽  
Fractional Quantum ◽  
C 73 ◽  
Fractional Parameter

AbstractThis paper investigates whether the framework of fractional quantum mechanics can broaden our perspective of black hole thermodynamics. Concretely, we employ a space-fractional derivative (Riesz in Acta Math 81:1, 1949) as our main tool. Moreover, we restrict our analysis to the case of a Schwarzschild configuration. From a subsequently modified Wheeler–DeWitt equation, we retrieve the corresponding expressions for specific observables. Namely, the black hole mass spectrum, M, its temperature T, and entropy, S. We find that these bear consequential alterations conveyed through a fractional parameter, $$\alpha $$ α . In particular, the standard results are recovered in the specific limit $$\alpha =2$$ α = 2 . Furthermore, we elaborate how generalizations of the entropy-area relation suggested by Tsallis and Cirto (Eur Phys J C 73:2487, 2013) and Barrow (Phys Lett B 808:135643, 2020) acquire a complementary interpretation in terms of a fractional point of view. A thorough discussion of our results is presented.

scholarly journals Broadening quantum cosmology with a fractional whirl

2021 ◽  
pp. 2140005
Author(s):  
S. M. M. Rasouli ◽  
S. Jalalzadeh ◽  
P. V. Moniz
Keyword(s):  
Quantum Mechanics ◽  
Fractional Calculus ◽  
Quantum Cosmology ◽  
Cosmological Solution ◽  
Isotropic Universe ◽  
Fractional Quantum ◽  
Stiff Matter ◽  
Standard Quantum

We start by presenting a brief summary of fractional quantum mechanics, as means to convey a motivation towards fractional quantum cosmology. Subsequently, such application is made concrete with the assistance of a case study. Specifically, we investigate and then discuss a model of stiff matter in a spatially flat homogeneous and isotropic universe. A new quantum cosmological solution, where fractional calculus implications are explicit, is presented and then contrasted with the corresponding standard quantum cosmology setting.

scholarly journals New scattering features in non-Hermitian space fractional quantum mechanics

2018 ◽  
Vol 396 ◽  
pp. 371-385 ◽  
Author(s):  
Mohammad Hasan ◽  
Bhabani Prasad Mandal
Keyword(s):  
Quantum Mechanics ◽  
Fractional Quantum ◽  
Hermitian Space

scholarly journals Adaptation of Conformable Residual Power Series Scheme in Solving Nonlinear Fractional Quantum Mechanics Problems

2020 ◽  
Vol 10 (3) ◽  
pp. 890 ◽  
Author(s):  
Mohammed Shqair ◽  
Mohammed Al-Smadi ◽  
Shaher Momani ◽  
Essam El-Zahar
Keyword(s):  
Quantum Mechanics ◽  
Power Series ◽  
Quantum Physics ◽  
Taylor Series Expansion ◽  
Fractional Quantum ◽  
Analytical Technique ◽  
Different Types ◽  
Residual Power Series ◽  
Residual Errors ◽  
Residual Power

In this paper, the general state of quantum mechanics equations that can be typically expressed by nonlinear fractional Schrödinger models will be solved based on an attractive efficient analytical technique, namely the conformable residual power series (CRPS). The fractional derivative is considered in a conformable sense. The desired analytical solution is obtained using conformable Taylor series expansion through substituting a truncated conformable fractional series and minimizing its residual errors to extract a supportive approximate solution in a rapidly convergent fractional series. This adaptation can be implemented as a novel alternative technique to deal with many nonlinear issues occurring in quantum physics. The effectiveness and feasibility of the CRPS procedures are illustrated by verifying three realistic applications. The obtained numerical results and graphical consequences indicate that the suggested method is a convenient and remarkably powerful tool in solving different types of fractional partial differential models.

scholarly journals Fractional quantum mechanics in polariton condensates with velocity-dependent mass

2015 ◽  
Vol 92 (19) ◽  
Author(s):  
F. Pinsker ◽  
W. Bao ◽  
Y. Zhang ◽  
H. Ohadi ◽  
A. Dreismann ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Fractional Quantum ◽  
Dependent Mass

scholarly journals Kajian Integral Lintasan Levy dalam Mekanika Kuantum Fraksional untuk Membentuk Persamaan Schrodinger Fraksional

2020 ◽  
Vol 5 (1) ◽  
pp. 80-86
Author(s):  
Chandra Halim ◽  
M. Farchani Rosyid
Keyword(s):  
Stochastic Process ◽  
Quantum Mechanics ◽  
Fractal Dimension ◽  
Schrödinger Equation ◽  
Path Integral ◽  
Schrodinger Equation ◽  
Fractional Quantum ◽  
Standard Quantum ◽  
Fractional Schrödinger Equation ◽  
Fractional Schrodinger Equation

The implementation of Lévy path integral generated by Lévy stochastic process on fractional Schrödinger equation has been investigated in the framework of fractional quantum mechanics. As the comparison, the implementation of Feynmann path integral generated by Wiener stochastic process on Schrödinger equation also has been investigated in the framework of standard quantum mechanics. There are two stochastic processes. There are Lévy stochastic and Wiener stochastic process. Both of them are able to produce fractal. In fractal’s concept, there is a value known as fractal dimension. The implementation of fractal dimension is the diffusion equation obtained by using Fokker Planck equation. In this paper, Lévy and Wiener fractal dimension have been obtained. There are  for Lévy and 2 for Wiener/Brown fractal dimension. Fractional quantum mechanics is generalization of standard quantum mechanics. A fractional quantum mechanics state is represented by wave function from fractional Schrödinger equation. Fractional Schrödinger equation is obtained by using kernel of Lévy path integral generated by Lévy stochastic process. Otherwise, standard quantum mechanics state is represented by wave function from standard Schrödinger equation. Standard Schrödinger equation is obtained by using kernel of Feynmann path integral generated by Wiener/Brown stochastic process.  Both Lévy and Feynmann Kernel have been investigated and the outputs are the Fourier Integral momentum phase of those kernels. We find that the forms of those kernels have similiraty. Therefore, we obtain Schrödinger equation from Lévy and Feynmann Kernel and also the comparison of Lévy energy in fractional quantum mechanics and particle energy in standard quantum mechanics.

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