scholarly journals Quantum mechanics with geometric constraints of Friedmann type

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 551-556 ◽  
Author(s):  
Tatiana Lasukova ◽  
Vladimir Lasukov ◽  
Maria Abdrashitova
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Free Particle ◽  
Geometric Constraints ◽  
Geometrical Constraints ◽  
Quantum Geometrodynamics

AbstractThe paper presents the study of quantum mechanics of a free particle with the constraints in the phase space, the canonical equations, which are the geometrical constraints of Friedmann type. It has been proved that the constraints can imitate force. As well as in quantum geometrodynamics with Logunov constraints, in quantum mechanics with constraints time does not vanish

scholarly journals A Quantum Space behind Simple Quantum Mechanics

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Chuan Sheng Chew ◽  
Otto C. W. Kong ◽  
Jason Payne
Keyword(s):  
Quantum Mechanics ◽  
Theoretical Model ◽  
Phase Space ◽  
Configuration Space ◽  
Center Of Mass ◽  
Free Particle ◽  
Physical Space ◽  
Dimensional Manifold ◽  
Quantum Space ◽  
Simple Quantum

In physics, experiments ultimately inform us about what constitutes a good theoretical model of any physical concept: physical space should be no exception. The best picture of physical space in Newtonian physics is given by the configuration space of a free particle (or the center of mass of a closed system of particles). This configuration space (as well as phase space) can be constructed as a representation space for the relativity symmetry. From the corresponding quantum symmetry, we illustrate the construction of a quantum configuration space, similar to that of quantum phase space, and recover the classical picture as an approximation through a contraction of the (relativity) symmetry and its representations. The quantum Hilbert space reduces into a sum of one-dimensional representations for the observable algebra, with the only admissible states given by coherent states and position eigenstates for the phase and configuration space pictures, respectively. This analysis, founded firmly on known physics, provides a quantum picture of physical space beyond that of a finite-dimensional manifold and provides a crucial first link for any theoretical model of quantum space-time at levels beyond simple quantum mechanics. It also suggests looking at quantum physics from a different perspective.

scholarly journals TRACE OF PHASE-SPACE NONCOMMUTATIVITY IN RESPONSE OF A FREE PARTICLE TO LINEARIZED GRAVITATIONAL WAVES

2013 ◽  
Vol 28 (35) ◽  
pp. 1350161 ◽  
Author(s):  
SUNANDAN GANGOPADHYAY ◽  
ANIRBAN SAHA ◽  
SWARUP SAHA
Keyword(s):  
Phase Space ◽  
Gravitational Waves ◽  
Cross Correlation ◽  
Free Particle ◽  
Momentum Scale ◽  
Specific Frequency ◽  
Global Nature ◽  
Space Noncommutativity ◽  
Correlation Procedure ◽  
Noncommutative Parameter

Interaction of linearized gravitational waves with a otherwise free particle has been studied quantum mechanically in a noncommutative (NC) phase-space to examine whether the particle's response to the gravitational wave gets modified due to spatial and/or momentum noncommutativity. The result shows that momentum noncommutativity introduces a oscillatory noise with a specific frequency determined by the fundamental momentum scale and particle mass. Because of the global nature of the phase-space noncommutativity such noise will have similar characteristics for all detector sites and thus will stand out in a data cross-correlation procedure. If detected, this noise will provide evidence of momentum noncommutativity and also an estimation of the relevant noncommutative parameter.

scholarly journals Quantum backflow in solutions to the Dirac equation of the spin-1 2 free particle

2018 ◽  
Vol 33 (32) ◽  
pp. 1850186 ◽  
Author(s):  
Hong-Yi Su ◽  
Jing-Ling Chen
Keyword(s):  
Quantum Mechanics ◽  
Dirac Equation ◽  
Relativistic Particle ◽  
Relativistic Quantum ◽  
Free Particle ◽  
Negative Energy ◽  
Dirac Particle ◽  
Relativistic Quantum Mechanics ◽  
Probability Current ◽  
Negative Probability

It was known that a free, non-relativistic particle in a superposition of positive momenta can, in certain cases, bear a negative probability current — hence termed quantum backflow. Here, it is shown that more variations can be brought about for a free Dirac particle, particularly when negative-energy solutions are taken into account. Since any Dirac particle can be understood as an antiparticle that acts oppositely (and vice versa), quantum backflow is found to arise in the superposition (i) of a well-defined momentum but different signs of energies, or more remarkably (ii) of different signs of both momenta and energies. Neither of these cases has a counterpart in non-relativistic quantum mechanics. A generalization by using the field-theoretic formalism is also presented and discussed.

Quantum Mechanics

2017 ◽  
Author(s):  
Nicholas Manton ◽  
Nicholas Mee
Keyword(s):  
Quantum Mechanics ◽  
Ground State ◽  
Variational Principles ◽  
Free Particle ◽  
Uncertainty Relations ◽  
Probabilistic Interpretation ◽  
Historical Account ◽  
Potential Wells ◽  
Harmonic Oscillator Potential ◽  
Ground State Energies

In this chapter, the main features of quantum theory are presented. The chapter begins with a historical account of the invention of quantum mechanics. The meaning of position and momentum in quantum mechanics is discussed and non-commuting operators are introduced. The Schrödinger equation is presented and solved for a free particle and for a harmonic oscillator potential in one dimension. The meaning of the wavefunction is considered and the probabilistic interpretation is presented. The mathematical machinery and language of quantum mechanics are developed, including Hermitian operators, observables and expectation values. The uncertainty principle is discussed and the uncertainty relations are presented. Scattering and tunnelling by potential wells and barriers is considered. The use of variational principles to estimate ground state energies is explained and illustrated with a simple example.

Invariance Groups in Classical and Quantum Mechanics

1973 ◽  
Vol 28 (3-4) ◽  
pp. 538-540 ◽  
Author(s):  
D. J. Simms
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Energy Levels ◽  
Classical Mechanics ◽  
Symmetry Groups ◽  
Casimir Invariants ◽  
Classical Phase Space ◽  
Invariance Groups ◽  
Classical And Quantum Mechanics

AbstractThis is a report on some new relations and analogies between classical mechanics and quantum mechanics which arise out of the work of Kostant and Souriau. Topics treated are i) the role of symmetry groups; ii) the notion of elementary system and the role of Casimir invariants; iii) energy levels; iv) quantisation in terms of geometric data on the classical phase space. Some applications are described.

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