Some implications of position-dependent mass quantum fractional Hamiltonian in quantum mechanics

2019 ◽  
Vol 134 (5) ◽  
Author(s):  
Rami Ahmad El-Nabulsi
Keyword(s):  
Quantum Mechanics ◽  
Dependent Mass ◽  
Position Dependent Mass

Path integral for quantum dynamics with position-dependent mass within the displacement operator approach

2020 ◽  
Vol 35 (30) ◽  
pp. 2050246
Author(s):  
H. Benzair ◽  
M. Merad ◽  
T. Boudjedaa
Keyword(s):  
Quantum Mechanics ◽  
Path Integral ◽  
Quantum Dynamics ◽  
Translation Operator ◽  
Integral Approach ◽  
Operator Approach ◽  
Square Well ◽  
Dependent Mass ◽  
Position Dependent Mass ◽  
Coulomb Potentials

In the context of quantum mechanics reformulated in a modified Hilbert space, we can formulate the Feynman’s path integral approach for the quantum systems with position-dependent mass particle using the formulation of position-dependent infinitesimal translation operator. Which is similar a deformed quantum mechanics based on modified commutation relations. An illustration of calculation is given in the case of the harmonic oscillator, the infinite square well and the inverse square plus Coulomb potentials.

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

2014 ◽  
Vol 55 (8) ◽  
pp. 082103 ◽  
Author(s):  
Héctor M. Moya-Cessa ◽  
Francisco Soto-Eguibar ◽  
Demetrios N. Christodoulides
Keyword(s):  
Quantum Mechanics ◽  
Operator Approach ◽  
Dependent Mass ◽  
Position Dependent Mass

On a new fractional uncertainty relation and its implications in quantum mechanics and molecular physics

2020 ◽  
Vol 476 (2234) ◽  
pp. 20190729 ◽  
Author(s):  
Rami Ahmad El-Nabulsi
Keyword(s):  
Quantum Mechanics ◽  
Regularization Method ◽  
Uncertainty Relation ◽  
Dimensional Regularization ◽  
Molecular Physics ◽  
Gradient Operator ◽  
Generalized Uncertainty Relation ◽  
New Form ◽  
Dependent Mass ◽  
Position Dependent Mass

A new generalized uncertainty relation is constructed based on Li-Ostoja-Starzewski fractional gradient operator of order 0 <  α  ≤ 1 introduced recently in literature which is motivated from dimensional regularization method. The new generalized uncertainty relation leads to a new form of Schrödinger equation and emergent position-dependent mass. Special forms of position-dependent mass were studied and the problem of a particle in a box was explored. Dissimilar forms of allowed quantum energies were obtained which lead to different scenarios. We have confronted the theory with observations by evaluating the maximum wavelength obtained in the 1,3-butadiene molecule. Several features were discussed accordingly.

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