scholarly journals Potential algebra approach to quantum mechanics with generalized uncertainty principle

2019 ◽  
Vol 383 (33) ◽  
pp. 125953
Author(s):  
Satoshi Ohya ◽  
Pinaki Roy
Keyword(s):  
Quantum Mechanics ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Algebra Approach

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.

scholarly journals Generalized uncertainty principle and its implications on geometric phases in quantum mechanics

2021 ◽  
Vol 136 (2) ◽  
Author(s):  
Giuseppe Gaetano Luciano ◽  
Luciano Petruzziello
Keyword(s):  
Quantum Mechanics ◽  
Phase Shift ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Upper Bounds ◽  
The Other ◽  
Quantum Mechanical ◽  
Geometric Phases ◽  
Deformation Parameters ◽  
Aharonov Bohm

AbstractWe study the implications of the generalized uncertainty principle (GUP) with a minimal measurable length on some quantum mechanical interferometry phenomena, such as the Aharonov–Bohm, Aharonov–Casher, COW and Sagnac effects. By resorting to a modified Schrödinger equation, we evaluate the lowest-order correction to the phase shift of the interference pattern within two different GUP frameworks: the first one is characterized by the redefinition of the physical momentum only, and the other is a Lorentz covariant GUP which also predicts non-commutativity of spacetime. The obtained results allow us to fix upper bounds on the GUP deformation parameters which may be tested through future high-precision interferometry experiments.

An uncertainty principle for the basic wavelet transform

2021 ◽  
pp. 2150002
Author(s):  
Javid Ahmad Ganie ◽  
Renu Jain
Keyword(s):  
Quantum Mechanics ◽  
Wavelet Transform ◽  
Weight Function ◽  
Uncertainty Principle ◽  
Signal Analysis ◽  
Integral Transform ◽  
Generalized Uncertainty Principle ◽  
Basic Wavelet ◽  
And Performance ◽  
Definition Of

The aim of this paper is to derive the uncertainty principle which has implications in signal analysis and in quantum mechanics. First, we derive the definition of the wavelet transform in [Formula: see text]-calculus by using some weight function. Certain properties like linearity, scaling, translation, etc. were discussed. Later on, to illustrate this integral transform several results were derived for the effectiveness and performance of the proposed method. Also, this paper surveys recent applications to establish generalized uncertainty principle.

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