scholarly journals Relativistic quantum-mechanical Brayton engine of the massless boson particle confined in the square well

2020 ◽  
Author(s):  
Fikri Abdillah ◽  
Yohanes Dwi Saputra
Keyword(s):  
Relativistic Quantum ◽  
Quantum Mechanical ◽  
Square Well ◽  
Massless Boson

scholarly journals Quantum speed limit for a relativistic electron in the noncommutative phase space

2017 ◽  
Vol 32 (23n24) ◽  
pp. 1750143 ◽  
Author(s):  
Kang Wang ◽  
Yu-Fei Zhang ◽  
Qing Wang ◽  
Zheng-Wen Long ◽  
Jian Jing
Keyword(s):  
Relativistic Electron ◽  
Uniform Magnetic Field ◽  
Lorentz Invariance ◽  
Relativistic Quantum ◽  
Quantum Mechanical ◽  
Speed Limit ◽  
Speed Of Light ◽  
Minimum Evolution ◽  
Noncommutative Phase Space ◽  
Average Speed

The influence of the noncommutativity on the average speed of a relativistic electron interacting with a uniform magnetic field within the minimum evolution time is investigated. We find that it is possible for the wave packet of the electron to travel faster than the speed of light in vacuum because of the noncommutativity. It is a clear signature of violating Lorentz invariance in the noncommutative relativistic quantum mechanical region.

scholarly journals The Einstein–Infeld–Hoffmann legacy in mathematical relativity II. Quantum laws of motion for singularities of spacetime

2019 ◽  
Vol 28 (11) ◽  
pp. 1930018
Author(s):  
A. Shadi Tahvildar-Zadeh ◽  
Michael K. H. Kiessling
Keyword(s):  
Finite Number ◽  
Relativistic Quantum ◽  
Quantum Mechanical ◽  
Mechanical Theory ◽  
Quantum Mechanical Theory ◽  
Theory Of Motion ◽  
Recent Developments ◽  
Laws Of Motion

We report on recent developments toward a relativistic quantum-mechanical theory of motion for a fixed, finite number of electrons, photons and their anti-particles, as well as its possible generalizations to other particles and interactions.

scholarly journals Complex square well - a new exactly solvable quantum mechanical model

1999 ◽  
Vol 32 (39) ◽  
pp. 6771-6781 ◽  
Author(s):  
Carl M Bender ◽  
Stefan Boettcher ◽  
H F Jones ◽  
Van M Savage
Keyword(s):  
Mechanical Model ◽  
Quantum Mechanical ◽  
Quantum Mechanical Model ◽  
Exactly Solvable ◽  
Solvable Quantum ◽  
Square Well

scholarly journals Siewert solutions of transcendental equations, generalized Lambert functions and physical applications

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 232-242 ◽  
Author(s):  
Victor Barsan
Keyword(s):  
Solar Energy ◽  
Energy Conversion ◽  
Analytical Methods ◽  
Systematic Approach ◽  
Relativistic Quantum ◽  
Classical Mechanics ◽  
Quantum Mechanical ◽  
Elementary Functions ◽  
Transcendental Equations ◽  
Lambert Functions

Abstract Several classes of transcendental equations, mainly eigenvalue equations associated to non-relativistic quantum mechanical problems, are analyzed. Siewert’s systematic approach of such equations is discussed from the perspective of the new results recently obtained in the theory of generalized Lambert functions and of algebraic approximations of various special or elementary functions. Combining exact and approximate analytical methods, quite precise analytical outputs are obtained for apparently untractable problems. The results can be applied in quantum and classical mechanics, magnetism, elasticity, solar energy conversion, etc.

scholarly journals Gauge-Independent Theory of Symmetry. II.

1965 ◽  
Vol 18 (2) ◽  
pp. 109 ◽  
Author(s):  
HA Buchdahl ◽  
LJ Tassie
Keyword(s):  
Relativistic Quantum ◽  
Classical Mechanics ◽  
Equation Of Motion ◽  
Symmetry Operation ◽  
Quantum Mechanical ◽  
Translation Invariant ◽  
Translation Operators ◽  
Physical Symmetry ◽  
Magnetic Translation ◽  
Quantum Mechanical Systems

This paper develops a gauge-independent symmetry theory of non-relativistic quantum mechanical systems, in line with that previously considered in the context of classical mechanics. We first discuss at length the motivation for adopting the view that the invariance of a system K under a physical symmetry operation .<I' should be taken to mean invariance of the equation of motion of K under a certain gauge-independent unitary transformation U c( .<1'). The formal development of the theory is then carried through, and some detailed examples are presented. In particular, corresponding to every direction along which a system K happens to be translation invariant there exists a gauge-independent generator of translations which leaves K invariant but which is not, in general, a component of either the canonical or the kinetic momentum. The connexion between such invariant generators of translations and the so-called magnetic translation operators is referred to.

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