scholarly journals Some consequences of the generalized uncertainty principle induced ultraviolet wave-vector cutoff in one-dimensional quantum mechanics

2013 ◽  
Vol 87 (8) ◽  
Author(s):  
K. Sailer ◽  
Z. Péli ◽  
S. Nagy
Keyword(s):  
Quantum Mechanics ◽  
Uncertainty Principle ◽  
Wave Vector ◽  
Generalized Uncertainty Principle ◽  
One Dimensional

scholarly journals A CLASS OF GUP SOLUTIONS IN DEFORMED QUANTUM MECHANICS

2010 ◽  
Vol 19 (12) ◽  
pp. 2003-2009 ◽  
Author(s):  
POURIA PEDRAM
Keyword(s):  
Black Hole ◽  
Quantum Mechanics ◽  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Loop Quantum Gravity ◽  
Black Hole Physics ◽  
Generalized Uncertainty Principle ◽  
Heisenberg Uncertainty Principle ◽  
Deformed Algebra ◽  
Heisenberg Uncertainty

Various candidates of quantum gravity such as string theory, loop quantum gravity and black hole physics all predict the existence of a minimum observable length which modifies the Heisenberg uncertainty principle to the so-called generalized uncertainty principle (GUP). This approach results from the modification of the commutation relations and changes all Hamiltonians in quantum mechanics. In this paper, we present a class of physically acceptable solutions for a general commutation relation without directly solving the corresponding generalized Schrödinger equations. These solutions satisfy the boundary conditions and exhibit the effect of the deformed algebra on the energy spectrum. We show that this procedure prevents us from doing equivalent but lengthy calculations.

The generalized uncertainty principle with commuting coordinates

2019 ◽  
Vol 34 (33) ◽  
pp. 1950267
Author(s):  
Won Sang Chung
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Three Dimensional ◽  
One Dimension ◽  
Momentum Representation ◽  
Position Representation

In this paper, we present a new D-dimensional generalized uncertainty principle (GUP) algebra with commuting coordinates which recovers [Formula: see text] in one dimension. We find two representations for this GUP: momentum representation and position representation. We discuss the GUP-corrected three-dimensional quantum mechanics in position representation for a small [Formula: see text]. Finally, we discuss the momentum wave function and GUP-corrected Fermi metal theory.

Scattering state in GUP by Milne’s differential equation

2018 ◽  
Vol 33 (39) ◽  
pp. 1850231 ◽  
Author(s):  
A. Armat ◽  
S. Mohammad Moosavi Nejad
Keyword(s):  
Differential Equation ◽  
Dirac Equation ◽  
Nonlinear Differential Equation ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Minimal Length ◽  
Nuclear Potential ◽  
Saxon Potential ◽  
One Dimensional ◽  
Scattering State

In this paper, our main aim is to obtain the transmission (T) and the reflection (R) coefficients for one-dimensional scattering state of the spin-[Formula: see text] particles in an interaction with a special nuclear potential. For this reason, at first, we consider Dirac equation and then obtain the Milne’s nonlinear differential equation due to minimal length from Schrödinger-like equation and then calculate the T- and R-coefficients using one-dimensional Woods–Saxon potential on the basis of the generalized uncertainty principle. Finally, we will check the validity and the correctness of our results.

Quantum mechanics on (anti)-de Sitter background

2017 ◽  
Vol 32 (26) ◽  
pp. 1750138 ◽  
Author(s):  
Won Sang Chung ◽  
Hassan Hassanabadi
Keyword(s):  
Quantum Mechanics ◽  
Harmonic Oscillator ◽  
Uncertainty Principle ◽  
De Sitter ◽  
One Dimensional ◽  
Sitter Background ◽  
Extended Uncertainty

In this paper, the quantum mechanics on the (anti) de Sitter background is investigated. the extended uncertainty principle and the deformed calculus are discussed for the quantum mechanics on the (anti)-de Sitter background. As examples one-dimensional box problem and one-dimensional harmonic oscillator problem are discussed.

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