Diffusion Process Representations for a Scalar-Field Schrödinger Equation Solution in Rotating Coordinates

2018 ◽  
pp. 241-268 ◽  
Author(s):  
William M. McEneaney ◽  
Ruobing Zhao
Keyword(s):  
Scalar Field ◽  
Schrödinger Equation ◽  
Diffusion Process ◽  
Schrodinger Equation ◽  
Equation Solution ◽  
Rotating Coordinates

Finite‐Temperature Schrodinger Equation: Solution in Coordinate Space

1998 ◽  
Vol 503 (1) ◽  
pp. 446-449 ◽  
Author(s):  
G. P. Malik ◽  
Raman Kumar Jha ◽  
Vijaya S. Varma
Keyword(s):  
Schrödinger Equation ◽  
Finite Temperature ◽  
Schrodinger Equation ◽  
Coordinate Space ◽  
Equation Solution

scholarly journals Entire Solutions to Nonlinear Scalar Field Equations with Indefinite Linear Part

2012 ◽  
Vol 12 (2) ◽  
Author(s):  
Gilles Evéquoz ◽  
Tobias Weth
Keyword(s):  
Scalar Field ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Linear Part ◽  
Continuous Functions ◽  
Entire Solutions ◽  
Field Equations ◽  
Nonlinear Scalar Field ◽  
Scalar Field Equations ◽  
Semilinear Schrödinger Equation

AbstractWe consider the stationary semilinear Schrödinger equation−Δu + a(x)u = f (x, u), u ∈ Hwhere a and f are continuous functions converging to some limits a

Schrödinger wave functional of a quantum scalar field in static space-times from precanonical quantization

2019 ◽  
Vol 16 (02) ◽  
pp. 1950017 ◽  
Author(s):  
I. V. Kanatchikov
Keyword(s):  
Scalar Field ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Delta Function ◽  
Functional Derivative ◽  
Field Configuration ◽  
Space Time ◽  
Schrödinger Representation ◽  
Limiting Case ◽  
Static Space

The functional Schrödinger representation of a scalar field on an [Formula: see text]-dimensional static space-time background is argued to be a singular limiting case of the hypercomplex quantum theory of the same system obtained by the precanonical quantization based on the space-time symmetric De Donder–Weyl Hamiltonian theory. The functional Schrödinger representation emerges from the precanonical quantization when the ultraviolet parameter [Formula: see text] introduced by precanonical quantization is replaced by [Formula: see text], where [Formula: see text] is the time-like tangent space Dirac matrix and [Formula: see text] is an invariant spatial [Formula: see text]-dimensional Dirac’s delta function whose regularized value at [Formula: see text] is identified with the cutoff of the volume of the momentum space. In this limiting case, the Schrödinger wave functional is expressed as the trace of the product integral of Clifford-algebra-valued precanonical wave functions restricted to a certain field configuration and the canonical functional derivative Schrödinger equation is derived from the manifestly covariant Dirac-like precanonical Schrödinger equation which is independent of a choice of a codimension-one foliation.

scholarly journals Lattice, Time-Dependent Schrödinger Equation Solution for Ion-Atom Collisions

1999 ◽  
Vol 82 (20) ◽  
pp. 3976-3979 ◽  
Author(s):  
D. R. Schultz ◽  
M. R. Strayer ◽  
J. C. Wells
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Time Dependent ◽  
Equation Solution

scholarly journals SEMICLASSICAL GRAVITY WITH A NONMINIMALLY COUPLED SCALAR FIELD

1995 ◽  
Vol 10 (15) ◽  
pp. 2231-2240 ◽  
Author(s):  
ABHIK KUMAR SANYAL
Keyword(s):  
Scalar Field ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Semiclassical Approximation ◽  
Matter Field ◽  
Leading Order ◽  
Coupling Constant ◽  
Wormhole Solution ◽  
Vacuum Einstein Equation ◽  
Curved Space

Semiclassical approximation to the Wheeler-DeWitt equation which corresponds to gravity with a nonminimally coupled scalar field is carried out. To the leading order, the vacuum Einstein equation, along with the functional Schrödinger equation for the matter field propagating in the background of classical curved space, is obtained. The Schrödinger equation is solved for a quartic potential. It is observed that the wave functional admits the wormhole boundary condition even for large negative values of the coupling constant ∊. For conformal coupling, ∊=1/6, the Hawking-Page wormhole solution is recovered.

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.

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