scholarly journals Solution of Non-Autonomous Schrödinger Equation for Quantized de Sitter Klein-Gordon Oscillator Modes Undergoing Attraction-Repulsion Transition

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 943
Author(s):  
Philip Broadbridge ◽  
Kathryn Deutscher
Keyword(s):  
Energy Spectrum ◽  
Scalar Field ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Canonical Quantization ◽  
Elementary Excitation ◽  
Accelerated Expansion ◽  
De Sitter ◽  
Discrete Energy ◽  
Klein Gordon

For a scalar field in an exponentially expanding universe, constituent modes of elementary excitation become unstable consecutively at shorter wavelength. After canonical quantization, a Bogoliubov transformation reduces the minimally coupled scalar field to independent 1D modes of two inequivalent types, leading eventually to a cosmological partitioning of energy. Due to accelerated expansion of the coupled space-time, each underlying mode transits from an attractive oscillator with discrete energy spectrum to a repulsive unit with continuous unbounded energy spectrum. The underlying non-autonomous Schrödinger equation is solved here as the wave function evolves through the attraction-repulsion transition and ceases to oscillate.

scholarly journals Time-covariant Schrödinger equation and invariant decay probability: the $$\Lambda $$-Kantowski–Sachs universe

2021 ◽  
Vol 81 (12) ◽  
Author(s):  
Theodoros Pailas ◽  
Nikolaos Dimakis ◽  
Petros A. Terzis ◽  
Theodosios Christodoulakis
Keyword(s):  
Schrödinger Equation ◽  
Wave Packet ◽  
Time Dependence ◽  
Schrodinger Equation ◽  
Canonical Quantization ◽  
Dynamical Equations ◽  
Quadratic Constraint ◽  
Decay Probability ◽  
Flrw Universe ◽  
Arbitrary Time Dependence

AbstractThe system under study is the $$\Lambda $$ Λ -Kantowski–Sachs universe. Its canonical quantization is provided based on a recently developed method: the singular minisuperspace Lagrangian describing the system, is reduced to a regular (by inserting into the dynamical equations the lapse dictated by the quadratic constraint) possessing an explicit (though arbitrary) time dependence; thus a time-covariant Schrödinger equation arises. Additionally, an invariant (under transformations $$t=f({\tilde{t}})$$ t = f ( t ~ ) ) decay probability is defined and thus “observers” which correspond to different gauge choices obtain, by default, the same results. The time of decay for a Gaussian wave packet localized around the point $$a=0$$ a = 0 (where a the radial scale factor) is calculated to be of the order $$\sim 10^{-42}{-}10^{-41}~\text {s}$$ ∼ 10 - 42 - 10 - 41 s . The acquired value is near the end of the Planck era (when comparing to a FLRW universe), during which the quantum effects are most prominent. Some of the results are compared to those obtained by following the well known canonical quantization of cosmological systems, i.e. the solutions of the Wheeler–DeWitt equation.

scholarly journals “Time”-Covariant Schrödinger Equation and the Canonical Quantization of the Reissner–Nordström Black Hole

2020 ◽  
Vol 2 (3) ◽  
pp. 414-441
Author(s):  
Theodoros Pailas
Keyword(s):  
Black Hole ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Canonical Quantization ◽  
Hamiltonian Density ◽  
Reduced Equations ◽  
Spacetime Singularity ◽  
Classical Singularity ◽  
Pp Wave ◽  
Do So

A “time”-covariant Schrödinger equation is defined for the minisuperspace model of the Reissner–Nordström (RN) black hole, as a “hybrid” between the “intrinsic time” Schrödinger and Wheeler–DeWitt (WDW) equations. To do so, a reduced, regular, and “time(r)”-dependent Hamiltonian density was constructed, without “breaking” the re-parametrization covariance r→f(r˜). As a result, the evolution of states with respect to the parameter r and the probabilistic interpretation of the resulting quantum description is possible, while quantum schemes for different gauge choices are equivalent by construction. The solutions are found for Dirac’s delta and Gaussian initial states. A geometrical interpretation of the wavefunctions is presented via Bohm analysis. Alongside this, a criterion is presented to adjudicate which, between two singular spacetimes, is “more” or “less” singular. Two ways to adjudicate the existence of singularities are compared (vanishing of the probability density at the classical singularity and semi-classical spacetime singularity). Finally, an equivalence of the reduced equations with those of a 3D electromagnetic pp-wave spacetime is revealed.

scholarly journals Covariant Variational Evolution and Jacobi brackets: Fields

2020 ◽  
Vol 35 (23) ◽  
pp. 2050206
Author(s):  
F. M. Ciaglia ◽  
F. Di Cosmo ◽  
A. Ibort ◽  
G. Marmo ◽  
L. Schiavone
Keyword(s):  
Schrödinger Equation ◽  
Variational Problem ◽  
Schrodinger Equation ◽  
Contact Geometry ◽  
Klein Gordon ◽  
Variational Evolution

The analysis of the covariant brackets on the space of functions on the solutions to a variational problem in the framework of contact geometry initiated in the companion letter[Formula: see text] is extended to the case of the multisymplectic formulation of the free Klein–Gordon theory and of the free Schrödinger equation.

Effects of a non-Hermitian potential on the Landau quantization

2019 ◽  
Vol 34 (12) ◽  
pp. 1950072 ◽  
Author(s):  
B. F. Ramos ◽  
I. A. Pedrosa ◽  
K. Bakke
Keyword(s):  
Magnetic Field ◽  
Energy Spectrum ◽  
Schrödinger Equation ◽  
Complex Potential ◽  
Schrodinger Equation ◽  
Uniform Magnetic Field ◽  
Spinless Particle ◽  
Symmetric Complex

In this work, we solve the time-independent Schrödinger equation for a Landau system modulated by a non-Hermitian Hamiltonian. The system consists of a spinless particle in a uniform magnetic field submitted to action of a non-[Formula: see text] symmetric complex potential. Although the Hamiltonian is neither Hermitian nor [Formula: see text]-symmetric, we find that the Landau problem under study exhibits an entirely real energy spectrum.

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