Dynamical Mappings of Density Operators in Quantum Mechanics. II. Time Dependent Mappings

1962 ◽  
Vol 3 (5) ◽  
pp. 848-852 ◽  
Author(s):  
Thomas F. Jordan ◽  
Mark A. Pinsky ◽  
E. C. G. Sudarshan
Keyword(s):  
Quantum Mechanics ◽  
Time Dependent ◽  
Density Operators

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.

scholarly journals Generation of Time-Independent and Time-Dependent Harmonic Oscillator-Like Potentials Using Supersymmetric Quantum Mechanics

2018 ◽  
Vol 4 (1) ◽  
pp. 47-55
Author(s):  
Timothy Brian Huber
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Mechanical System ◽  
Schrodinger Equation ◽  
Supersymmetric Quantum Mechanics ◽  
Time Dependent ◽  
Quantum Mechanical ◽  
Quantum Mechanical System ◽  
Intertwining Operator

The harmonic oscillator is a quantum mechanical system that represents one of the most basic potentials. In order to understand the behavior of a particle within this system, the time-independent Schrödinger equation was solved; in other words, its eigenfunctions and eigenvalues were found. The first goal of this study was to construct a family of single parameter potentials and corresponding eigenfunctions with a spectrum similar to that of the harmonic oscillator. This task was achieved by means of supersymmetric quantum mechanics, which utilizes an intertwining operator that relates a known Hamiltonian with another whose potential is to be built. Secondly, a generalization of the technique was used to work with the time-dependent Schrödinger equation to construct new potentials and corresponding solutions.

scholarly journals CLASSICAL AND QUANTUM TIME DEPENDENT SOLUTIONS IN STRING THEORY

2004 ◽  
Vol 19 (32) ◽  
pp. 5651-5661 ◽  
Author(s):  
C. MARTÍNEZ-PRIETO ◽  
O. OBREGÓN ◽  
J. SOCORRO
Keyword(s):  
Quantum Mechanics ◽  
Effective Action ◽  
Scalar Fields ◽  
Time Dependent ◽  
Interpretation Of Quantum Mechanics ◽  
Quantum Time ◽  
Dependent Model ◽  
Classical Behavior ◽  
Time Dependent Model ◽  
Friedmann Robertson Walker

Using the ontological interpretation of quantum mechanics in a particular sense, we obtain the classical behavior of the scale factor and two scalar fields, derived from a string effective action for the Friedmann–Robertson–Walker (FRW) time dependent model. Besides, the Wheeler–DeWitt equation is solved exactly. We speculate that the same procedure could also be applied to S-branes.

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