scholarly journals On the Relativistic Quantum Mechanics of a Particle in Space with Minimal Length

2012 ◽  
Vol 57 (9) ◽  
pp. 942
Author(s):  
Ch.M. Scherbakov
Keyword(s):  
Quantum Mechanics ◽  
Commutation Relation ◽  
Relativistic Quantum ◽  
Heisenberg Algebra ◽  
Minimal Length ◽  
Group Symmetry ◽  
Relativistic Quantum Mechanics ◽  
Noncommutative Space ◽  
Quantum Mechanical

A noncommutative space and the deformed Heisenberg algebra [X,P] = iħ{1 – βP2}1/2 are investigated. The quantum mechanical structures underlying this commutation relation are studied. The rotational group symmetry is discussed in detail.

Probability relations between separated systems

1936 ◽  
Vol 32 (3) ◽  
pp. 446-452 ◽  
Author(s):  
E. Schrödinger
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Pure State ◽  
Relativistic Quantum ◽  
Present Theory ◽  
Relativistic Quantum Mechanics ◽  
Quantum Mechanical ◽  
Alternative Possibility ◽  
Linearly Independent ◽  
Statistical Operator

The paper first scrutinizes thoroughly the variety of compositions which lead to the same quantum-mechanical mixture (as opposed to state or pure state). With respect to a given mixture every state has a definite probability (or mixing fraction) between 0 and 1 (including the limits), which is calculated from the mixtures Statistical Operator and the wave function of the state in question.A well-known example of mixtures occurs when a system consists of two separated parts. If the wave function of the whole system is known, either part is in the situation of a mixture, which is decomposed into definite constituents by a definite measuring programme to be carried out on the other part. All the conceivable decompositions (into linearly independent constituents) of the first system are just realized by all the possible measuring programmes that can be carried out on the second one. In general every state of the first system can be given a finite chance by a suitable choice of the programme.It is suggested that these conclusions, unavoidable within the present theory but repugnant to some physicists including the author, are caused by applying non-relativistic quantum mechanics beyond its legitimate range. An alternative possibility is indicated.

EFFECT OF MAXIMUM MOMENTUM ON QUANTUM MECHANICAL SCATTERING AND BOUND STATES

2013 ◽  
Vol 28 (15) ◽  
pp. 1350061 ◽  
Author(s):  
CHEE-LEONG CHING ◽  
RAJESH R. PARWANI
Keyword(s):  
Quantum Mechanics ◽  
Bound States ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics ◽  
Quantum Mechanical ◽  
Position Uncertainty ◽  
Exact Position ◽  
Usual Quantum ◽  
Quantum Mechanical Scattering ◽  
Mechanical Scattering

We construct the exact position representation for a deformed (non-relativistic) quantum mechanics which exhibits an intrinsic maximum momentum and use it to study problems such as a particle in a box and an asymmetric well. In particular, we show that unlike usual quantum mechanics, the present deformed case delays the formation of bound states in a finite potential well, a distinguishing feature that might be relevant for empirical investigations. We also contrast our results with the string-motivated type of deformed quantum mechanics which incorporates a minimum position uncertainty rather than a maximum momentum.

scholarly journals Pseudoharmonic oscillator in quantum mechanics with a minimal length

2014 ◽  
Vol 29 (28) ◽  
pp. 1450143 ◽  
Author(s):  
Djamil Bouaziz ◽  
Abdelmalek Boukhellout
Keyword(s):  
Quantum Mechanics ◽  
Diatomic Molecules ◽  
Relativistic Quantum ◽  
Energy Levels ◽  
Generalized Uncertainty Principle ◽  
Minimal Length ◽  
Relativistic Quantum Mechanics ◽  
Perturbative Approach ◽  
Minimal Length Scale ◽  
Pseudoharmonic Oscillator

The pseudoharmonic oscillator potential is studied in non-relativistic quantum mechanics with a generalized uncertainty principle characterized by the existence of a minimal length scale, [Formula: see text]. By using a perturbative approach, we derive an analytical expression of the energy spectrum in the first-order of the minimal length parameter β. We investigate the effect of this fundamental length on the vibration–rotation energy levels of diatomic molecules through this potential function interaction. We explicitly show that the minimal length would have some physical importance in studying the spectra of diatomic molecules.

scholarly journals GRAVITOMAGNETIC MOMENTS AND DYNAMICS OF DIRAC (SPIN ½) FERMIONS IN FLAT SPACE–TIME MAXWELLIAN GRAVITY

2004 ◽  
Vol 19 (25) ◽  
pp. 4207-4229 ◽  
Author(s):  
HARIHAR BEHERA ◽  
P. C. NAIK
Keyword(s):  
Quantum Mechanics ◽  
Equivalence Principle ◽  
Relativistic Quantum ◽  
Flat Space ◽  
Space Time ◽  
Relativistic Quantum Mechanics ◽  
Quantum Mechanical ◽  
Gravitational Effects ◽  
Spin Particle ◽  
Dirac Spin

The gravitational effects in the relativistic quantum mechanics are investigated in a relativistically derived version of Heaviside's speculative gravity (in flat space–time) named here as "Maxwellian gravity." The standard Dirac's approach to the intrinsic spin in the fields of Maxwellian gravity yields the gravitomagnetic moment of a Dirac (spin ½) particle exactly equal to its intrinsic spin. Violation of the Equivalence Principle (both at classical and quantum-mechanical level) in the relativistic domain has also been reported in this work.

Quantum-mechanical, gravitating Kerr–Newton particles

1992 ◽  
Vol 439 (1906) ◽  
pp. 271-278 ◽  
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics ◽  
Quantum Mechanical ◽  
Twistor Theory ◽  
Theory Of Gravitation

Newton’s theory of gravitation is extended to allow for sources with spin. Ideas from twistor theory are used while the laplacian relation between source and potential is retained. The resulting gravitational potentials display singularity structures analogous to those found in Kerr’s solutions in general relativity. However, incorporating the effects of non-relativistic quantum mechanics removes the singularity for sources with spins 1/2, 3/2, 5/2...

Statistical properties of the q-deformed relativistic Dirac oscillator in minimal length quantum mechanics

2018 ◽  
Vol 96 (1) ◽  
pp. 25-29 ◽  
Author(s):  
S. Sargolzaeipor ◽  
H. Hassanabadi ◽  
W.S. Chung
Keyword(s):  
Magnetic Field ◽  
Quantum Mechanics ◽  
External Magnetic Field ◽  
Relativistic Quantum ◽  
Two Dimensions ◽  
Minimal Length ◽  
Statistical Properties ◽  
Relativistic Quantum Mechanics ◽  
Two Dimensional ◽  
Dirac Oscillator

In this article, we introduce a two-dimensional Dirac oscillator in the presence of an external magnetic field in terms of q-deformed creation and annihilation operators in the framework of relativistic quantum mechanics with minimal length. We discuss the eigenvalues of q-deformed Dirac oscillator in two dimensions and report the statistical quantities of the system for a small real q.

scholarly journals Exact Solutions of the (2+1)-Dimensional Dirac Oscillator under a Magnetic Field in the Presence of a Minimal Length in the Non-commutative Phase Space

2015 ◽  
Vol 70 (8) ◽  
pp. 619-627 ◽  
Author(s):  
Abdelmalek Boumali ◽  
Hassan Hassanabadi
Keyword(s):  
Magnetic Field ◽  
Quantum Mechanics ◽  
Phase Space ◽  
Hypergeometric Functions ◽  
Relativistic Quantum ◽  
Minimal Length ◽  
Wave Functions ◽  
Relativistic Quantum Mechanics ◽  
Two Dimensional ◽  
Dirac Oscillator

AbstractWe consider a two-dimensional Dirac oscillator in the presence of a magnetic field in non-commutative phase space in the framework of relativistic quantum mechanics with minimal length. The problem in question is identified with a Poschl–Teller potential. The eigenvalues are found, and the corresponding wave functions are calculated in terms of hypergeometric functions.

scholarly journals SEDEONIC GENERALIZATION OF RELATIVISTIC QUANTUM MECHANICS

2009 ◽  
Vol 24 (32) ◽  
pp. 6237-6254 ◽  
Author(s):  
VICTOR L. MIRONOV ◽  
SERGEY V. MIRONOV
Keyword(s):  
Quantum Mechanics ◽  
Relativistic Quantum ◽  
Space Time ◽  
Second Order ◽  
Wave Functions ◽  
Relativistic Quantum Mechanics ◽  
Noncommutative Space ◽  
Einstein Relation ◽  
First Order ◽  
Energy And Momentum

We represent sixteen-component values "sedeons," generating associative noncommutative space–time algebra. We demonstrate a generalization of relativistic quantum mechanics using sedeonic wave functions and sedeonic space–time operators. It is shown that the sedeonic second-order equation for the sedeonic wave function, obtained from the Einstein relation for energy and momentum, describes particles with spin 1/2. We showed that the sedeonic second-order wave equation can be reformulated in the form of the system of the first-order Maxwell-like equations for the massive fields. We proposed the sedeonic first-order equations analogous to the Dirac equation, which differ in space–time properties and describe several types of massive and massless particles. In particular we proposed four different equations, which could describe four types of neutrinos.

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