Non-Markovian analysis of the phase-damped Jaynes-Cummings model in the presence of a classical homogeneous gravitational field

AbstractA solution of Einstein's vacuum field equations, apparently new, is exhibited. The metric, which is homogeneous (that is, admits a three-parameter group of motions transitive on space-like hypersurfaces), belongs to Taub Type V. The canonical form of the Riemann tensor, which is of Petrov Type I, is determined.

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WKB FORMALISM AND A LOWER LIMIT FOR THE ENERGY EIGENSTATES OF BOUND STATES FOR SOME POTENTIALS

Modern Physics Letters A ◽

10.1142/s0217732307022979 ◽

2007 ◽

Vol 22 (35) ◽

pp. 2675-2687 ◽

Cited By ~ 1

Author(s):

LUIS F. BARRAGÁN-GIL ◽

ABEL CAMACHO

Keyword(s):

Quantum Mechanics ◽

Gravitational Field ◽

Lower Bound ◽

Harmonic Oscillator ◽

Approximation Method ◽

Bound States ◽

The Other ◽

Homogeneous Gravitational Field ◽

Definition Of ◽

Ground Energy

In this work the conditions appearing in the so-called WKB approximation formalism of quantum mechanics are analyzed. It is shown that, in general, a careful definition of an approximation method requires the introduction of two length parameters, one of them always considered in the textbooks on quantum mechanics, whereas the other is usually neglected. Afterwards we define a particular family of potentials and prove, resorting to the aforementioned length parameters, that we may find an energy which is a lower bound to the ground energy of the system. The idea is applied to the case of a harmonic oscillator and also to a particle freely falling in a homogeneous gravitational field, and in both cases the consistency of our method is corroborated. This approach, together with the so-called Rayleigh–Ritz formalism, allows us to define an energy interval in which the ground energy of any potential, belonging to our family, must lie.

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Relativistic quantum bouncing particles in a homogeneous gravitational field

International Journal of Modern Physics D ◽

10.1142/s021827182150098x ◽

2021 ◽

pp. 2150098

Author(s):

Ar Rohim ◽

Kazushige Ueda ◽

Kazuhiro Yamamoto ◽

Shih-Yuin Lin

Keyword(s):

Gravitational Field ◽

Relativistic Effect ◽

Relativistic Quantum ◽

Energy Levels ◽

Nonrelativistic Limit ◽

Wave Functions ◽

Dirac Equations ◽

Rindler Coordinates ◽

Klein Gordon ◽

Homogeneous Gravitational Field

In this paper, we study the relativistic effect on the wave functions for a bouncing particle in a gravitational field. Motivated by the equivalence principle, we investigate the Klein–Gordon and Dirac equations in Rindler coordinates with the boundary conditions mimicking a uniformly accelerated mirror in Minkowski space. In the nonrelativistic limit, all these models in the comoving frame reduce to the familiar eigenvalue problem for the Schrödinger equation with a fixed floor in a linear gravitational potential, as expected. We find that the transition frequency between two energy levels of a bouncing Dirac particle is greater than the counterpart of a Klein–Gordon particle, while both are greater than their nonrelativistic limit. The different corrections to eigen-energies of particles of different nature are associated with the different behaviors of their wave functions around the mirror boundary.

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