Ehrenfest theorem in relativistic quantum theory

• URL: http://arxiv.org/abs/2111.10798v2
• Date: Wed, 20 Apr 2022 19:21:22 GMT
• Title: Ehrenfest theorem in relativistic quantum theory
• Authors: Iwo Bialynicki-Birula and Zofia Bialynicka-Birula
• Abstract summary: We extend the classic Ehrenfest result to the relativistic domain by deriving directly Newton's second law. The derivation is based on the conservation laws for the energy and momentum.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Ehrenfest theorem is proven in relativistic quantum theory of charged particles, moving under the influence of an external electromagnetic field. In order to extend the classic Ehrenfest result to the relativistic domain we bypassed the problems with the relativistic position operator by deriving directly Newton's second law. Our approach is characterized by its universality. The detailed form of the wave equation is not needed. All that is required is the existence of the conserved electric four-current built from the particle wave function. The derivation is based on the conservation laws for the energy and momentum.

Related papers

• Self-consistency, relativism and many-particle system [0.0]
  Interrelation between concepts of self-consistency, relativism and many-particle systems is considered. Paper shows that quantum systems with a time independent function of quasi-density probability in phase space are not capable to emit electromagnetic radiation.
  arXiv  Detail & Related papers  (2024-04-21T08:38:40Z)
• Double-scale theory [77.34726150561087]
  We present a new interpretation of quantum mechanics, called the double-scale theory. It is based on the simultaneous existence of two wave functions in the laboratory reference frame. The external wave function corresponds to a field that pilots the center-of-mass of the quantum system. The internal wave function corresponds to the interpretation proposed by Edwin Schr"odinger.
  arXiv  Detail & Related papers  (2023-05-29T14:28:31Z)
• Correspondence Between the Energy Equipartition Theorem in Classical Mechanics and its Phase-Space Formulation in Quantum Mechanics [62.997667081978825]
  In quantum mechanics, the energy per degree of freedom is not equally distributed. We show that in the high-temperature regime, the classical result is recovered.
  arXiv  Detail & Related papers  (2022-05-24T20:51:03Z)
• On free fall of quantum matter [0.0]
  We show that free fall depends on quantum-matter properties. We then estimate the E"otv"os parameter for a pair of atoms freely falling near the Earth's surface.
  arXiv  Detail & Related papers  (2021-10-19T15:34:36Z)
• Wave-particle duality and the zitterbewegung [0.0]
  We show that a free spinless quantum particle moving with velocity v obeys the standard wave equation of electro-magnetism. We also discuss the implications for the zitterbewegung problem and its relationship to isotropy.
  arXiv  Detail & Related papers  (2021-07-19T17:17:26Z)
• Fresh look at the effects of gravitational tidal forces on a freely-falling quantum particle [0.0]
  We take a closer and new look at the effects of tidal forces on the free fall of a quantum particle inside a spherically symmetric gravitational field. We derive the corresponding Schr"odinger equation for the particle by starting from the fully relativistic Klein-Gordon equation.
  arXiv  Detail & Related papers  (2021-02-18T18:25:08Z)
• Hamiltonian Formulation of the Pilot-Wave Theory [0.0]
  In pilot-wave theory of quantum mechanics particles have definite positions and velocities and the system evolves deterministically. I first construct a Hamiltonian that gives Schrodinger's equation and the guidance equation for the particle. I then find the Hamiltonian for a relativistic particle in Dirac's theory and for a quantum scalar field.
  arXiv  Detail & Related papers  (2021-01-21T23:52:38Z)
• The Time-Evolution of States in Quantum Mechanics [77.34726150561087]
  It is argued that the Schr"odinger equation does not yield a correct description of the quantum-mechanical time evolution of states of isolated (open) systems featuring events. A precise general law for the time evolution of states replacing the Schr"odinger equation is formulated within the so-called ETH-Approach to Quantum Mechanics.
  arXiv  Detail & Related papers  (2021-01-04T16:09:10Z)
• Feynman Functional Integral in the Fokker Theory [62.997667081978825]
  equivalence of two formulations of Fokker's quantum theory is proved. The common basis for the two approaches is the generalized canonical form of Fokker's action.
  arXiv  Detail & Related papers  (2020-11-11T12:10:01Z)
• General quantum-mechanical solution for twisted electrons in a uniform magnetic field [68.8204255655161]
  A theory of twisted (and other structured) paraxial electrons in a uniform magnetic field is developed. The observable effect of a different behavior of relativistic Laguerre-Gauss beams with opposite directions of the orbital angular momentum penetrating from the free space into a magnetic field is predicted.
  arXiv  Detail & Related papers  (2020-05-13T16:35:10Z)
• External and internal wave functions: de Broglie's double-solution theory? [77.34726150561087]
  We propose an interpretative framework for quantum mechanics corresponding to the specifications of Louis de Broglie's double-solution theory. The principle is to decompose the evolution of a quantum system into two wave functions. For Schr"odinger, the particles are extended and the square of the module of the (internal) wave function of an electron corresponds to the density of its charge in space.
  arXiv  Detail & Related papers  (2020-01-13T13:41:24Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.