Time Dependent Quantum Mechanics with Correlated Coherent States

1992 ◽  
pp. 403-424
Author(s):  
Brian Weiner
Keyword(s):  
Quantum Mechanics ◽  
Coherent States ◽  
Time Dependent

scholarly journals A CLASS OF QUANTUM STATES WITH CLASSICAL-LIKE EVOLUTION

1994 ◽  
Vol 08 (29) ◽  
pp. 1823-1831 ◽  
Author(s):  
SALVATORE DE MARTINO ◽  
SILVIO DE SIENA ◽  
FABRIZIO ILLUMINATI
Keyword(s):  
Quantum Mechanics ◽  
Harmonic Oscillator ◽  
Coherent States ◽  
Quantum States ◽  
Time Dependent ◽  
Stationary States ◽  
Oscillator Potential ◽  
Classical Motion ◽  
Stochastic Formulation ◽  
New States

In the framework of the stochastic formulation of quantum mechanics we derive non-stationary states for a class of time-dependent potentials. The wave packets follow a classical motion with constant dispersion. The new states define a possible extension of the harmonic oscillator coherent states. As an explicit application, we study a sestic oscillator potential.

THE DEPENDENCY ON THE SQUEEZING PARAMETER FOR THE UNCERTAINTY RELATION IN THE SQUEEZED STATES OF THE TIME-DEPENDENT OSCILLATOR

2004 ◽  
Vol 18 (16) ◽  
pp. 2307-2324 ◽  
Author(s):  
JEONG RYEOL CHOI
Keyword(s):  
Quantum Mechanics ◽  
Coherent State ◽  
Coherent States ◽  
Uncertainty Relation ◽  
Time Dependent ◽  
Squeezed States ◽  
Time Dependency ◽  
Minimum Value ◽  
Number State

We obtained the uncertainty relation in squeezed states for a time-dependent oscillator. The uncertainty relation in coherent states is same as that of the number states with n=0. However, the uncertainty relation in squeezed states does not satisfy this property and depends on squeezing parameter c. For instance, the uncertainty relation is ℏ/2 which is the minimum value as far as quantum mechanics permits for c=1, same as that in coherent state for c=±∞, and infinity for c=-1. If the time-dependency of the Hamiltonian for the system vanishes, the uncertainty relation in squeezed states will no longer depend on c and becomes the same as that in number state with n=0, like the uncertainty relation in coherent states.

scholarly journals A new approximation method for time-dependent problems in quantum mechanics

2005 ◽  
Vol 340 (1-4) ◽  
pp. 87-93 ◽  
Author(s):  
Paolo Amore ◽  
Alfredo Aranda ◽  
Francisco M. Fernández ◽  
Hugh Jones
Keyword(s):  
Quantum Mechanics ◽  
Approximation Method ◽  
Time Dependent ◽  
Time Dependent Problems

Energy and Momentum Eigenspectrum of the Hulthén-screened Cosine Kratzer Potential Using Proper Quantization Rule and SUSYQM Method

2021 ◽  
Author(s):  
Kaushal R Purohit ◽  
Rajendrasinh H PARMAR ◽  
Ajay Kumar Rai
Keyword(s):  
Quantum Mechanics ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Numerical Data ◽  
Time Dependent ◽  
Quantization Rule ◽  
Approximation Approach ◽  
Momentum Spectra ◽  
Energy And Momentum ◽  
Three Dimensional Space

Abstract Using the Qiang-Dong proper quantization rule (PQR) and the supersymmetric quantum mechanics approach, we obtained the eigenspectrum of the energy and momentum for time independent and time dependent Hulthen-screened cosine Kratzer potentials. For the suggested time independent Hulthen-screened cosine Kratzer potential, we solved the Schrodinger equation in D dimensions (HSCKP). The Feinberg-Horodecki equation for time-dependent Hulthen-screened cosine Kratzer potential was also solved (tHSCKP). To address the inverse square term in the time independent and time dependent equations, we employed the Greene-Aldrich approximation approach. We were able to extract time independent and time dependent potentials, as well as their accompanying energy and momentum spectra. In three-dimensional space, we estimated the rotational vibrational (RV) energy spectrum for many homodimers ($H_2, I_2, O_2$) and heterodimers ($MnH, ScN, LiH, HCl$). We also used the recently introduced formula approach to obtain the relevant eigen function. We also calculated momentum spectra for the dimers $MnH$ and $ScN$. The method is compared to prior methodologies for accuracy and validity using numerical data for heterodimer $LiH, HCl$ and homodimer $I_2, O_2,H_2$. The calculated energy and momentum spectra are tabulated and analysed.

SUSY coherent states and enhanced canonical quantizations for Pauli model

2021 ◽  
pp. 2150105
Author(s):  
Jean Vignon Hounguevou ◽  
Daniel Sabi Takou ◽  
Gabriel Y. H. Avossevou
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Coherent States ◽  
Differential Operators ◽  
Canonical Quantization ◽  
Point Of View ◽  
Supersymmetric Quantum Mechanics ◽  
Geometric Properties

In this paper, we study coherent states for a quantum Pauli model through supersymmetric quantum mechanics (SUSYQM) method. From the point of view of canonical quantization, the construction of these coherent states is based on the very important differential operators in SUSYQM call factorization operators. The connection between classical and quantum theory is given by using the geometric properties of these states.

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