Generalized Gaussian wave packet dynamics, Schrödinger equation, and stationary phase approximation

1988 ◽  
Vol 89 (4) ◽  
pp. 2003-2014 ◽  
Author(s):  
Daniel Huber ◽  
Eric J. Heller ◽  
Robert G. Littlejohn
Keyword(s):  
Schrödinger Equation ◽  
Wave Packet ◽  
Stationary Phase ◽  
Schrodinger Equation ◽  
Gaussian Wave Packet ◽  
Phase Approximation ◽  
Wave Packet Dynamics

Solving Time-dependent Schrödinger Equation Using Gaussian Wave Packet Dynamics

2018 ◽  
Vol 73 (9) ◽  
pp. 1269-1278
Author(s):  
Min-Ho Lee ◽  
Chang Woo Byun ◽  
Nark Nyul Choi ◽  
Dae-Soung Kim
Keyword(s):  
Schrödinger Equation ◽  
Wave Packet ◽  
Schrodinger Equation ◽  
Time Dependent ◽  
Gaussian Wave Packet ◽  
Wave Packet Dynamics

scholarly journals Metaoptics with Nonrelativistic Matter Waves

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
T. Taillandier-Loize ◽  
J. Baudon ◽  
M. Hamamda ◽  
G. Dutier ◽  
V. Bocvarski ◽  
...  
Keyword(s):  
Schrödinger Equation ◽  
Wave Packet ◽  
Group Velocity ◽  
Schrodinger Equation ◽  
Atom Interferometry ◽  
Matter Waves ◽  
Wave Packet Dynamics

The counterpart of metamaterials in light optics for nonrelativistic matter waves governed by the Schrödinger equation can be found by transiently reversing the group velocity using a so called comoving potential. Possible applications to wave-packet dynamics, atom interferometry, and atom deceleration are described.

scholarly journals Two-particle Schrödinger equation animations of wave packet–wave packet scattering

2000 ◽  
Vol 68 (12) ◽  
pp. 1113-1119 ◽  
Author(s):  
Jon J. V. Maestri ◽  
Rubin H. Landau ◽  
Manuel J. Páez
Keyword(s):  
Schrödinger Equation ◽  
Wave Packet ◽  
Schrodinger Equation

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.

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