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Nonlinear Dynamics

Time-correlation function and average energy of molecules in presence of Deng-Fan potential in a moving boundary

Debraj Nath, Amlan K. Roy

Published Sep 16, 2022• 3 citations
Publisher

Abstract

Abstract For the Deng-Fan potential within a moving boundary condition, the time-dependent Schrödinger equation is considered analytically. The eigenvalue equation is solved by using a combination of Pekeris and Greene-Aldrich approximations. Various time-dependent quantities including density distribution function, auto-correlation function, disequilibrium, average energy, quantum similarity, quantum similarity index are obtained for selected eight diatomic molecules. The motion of the peak of soliton with moving boundary condition is investigated for ground states of some diatomic molecules along with the corresponding peak values.

DOI
10.1007/s11071-022-07664-4

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Abstract For the Deng-Fan potential within a moving boundary condition, the time-dependent Schrödinger equation is considered analytically. The eigenvalue equation is solved by using a combination of Pekeris and Greene-Aldrich approximations. Various time-dependent quantities including density distribution function, auto-correlation function, disequilibrium, average energy, quantum similarity, quantum similarity index are obtained for selected eight diatomic molecules. The motion of the peak of soliton with moving boundary condition is investigated for ground states of some diatomic molecules along with the corresponding peak values.
In this work, we present analytical solution of Schrödinger equation of confined pseudoharmonic potential in presence of a moving boundary condition, for an arbitrary angular momentum state. It turns out that an important quantity to probe the problem is internuclear distance ratio, which depends on the solution of Ermakov equation. The minimum value of time-dependent (TD) Heisenberg uncertainty product always remains greater than that of the minimum uncertainty product h/2. The TD average energy is derived analytically in a closed form and the corresponding average force and average pressure are defined. Moreover, time correlation function of two states for the case of six selected diatomic molecules (CO, NO, ScH, CH, H2, N2) is obtained. It is found to depend on internuclear distance ratio at two different time domains. The TD survival probability and average life-time of molecule in a confined quantum system are defined. Expressions are offered for quantum similarity measure, dissimilarity and quantum similarity index. The latter is given for a pair of molecules. The obtained results are compared with available literature, wherever possible. To our knowledge this is the first detailed report of a non-harmonic central potential in a TD moving boundary condition.
ABSTRACT In this work, we present an analytical solution of Schrödinger equation of confined pseudoharmonic potential in the presence of a moving boundary condition for an arbitrary angular momentum state. It turns out that an important quantity to probe the problem is the internuclear distance ratio, which depends on the solution of Ermakov equation. The minimum value of the time‐dependent (TD) Heisenberg uncertainty product always remains greater than that of the minimum uncertainty product . The TD average energy is derived analytically in a closed form, and the corresponding average force and average pressure are defined. Moreover, the time correlation function of two states for the case of six selected diatomic molecules (CO, NO, ScH, CH, , ) is obtained. It is found to depend on the internuclear distance ratio at two different time domains. The TD survival probability and average life‐time of a molecule in a confined quantum system are defined. Expressions are offered for quantum similarity measure, dissimilarity, and quantum similarity index. The latter is given for a pair of molecules. The obtained results are compared with available literature, wherever possible. To our knowledge this is the first detailed report of a non‐harmonic central potential in a TD moving boundary condition.
The bound state solutions of the Schrödinger equation with the rotating Deng-Fan molecular potential are presented approximately. It is shown that the solutions can be expressed by the generalized hypergeometric functions. The normalized wavefunctions are also derived. To show the accuracy of our results, the eigenvalues calculated numerically for arbitrary quantum numbers n and l with two different values of the parameter r e are in good agreement with those obtained by the MATHEMATICA package for short potential range.
Abstract The equation of Schrodinger is a fundamental mathematical framework used to clarify the motion of the wave form, which is a phenomenon in the field of quantum physics. A method's wave function contains the complete description of its particles. The computational solution of the Schrodinger problem is a multifaceted problem. The eigenvalues and typical functions of the modified Kratzer plus Hulthen potential were ascertained analytically in this study. This study used an estimating approach that Nikiforov-Uvarov functional analysis had suggested for dealing with the problem. Estimating energy spectra and applying the results to certain specific diatomic molecules was the aim. The excellent results obtained from this strategy were confirmed by comparing our eigenvalue data with additional numerical data that was gathered by other researchers.
Exact solutions of time-dependent Schrödinger equation in presence of time-dependent potential is defined by point transformation and separation of variables. Energy and Heisenberg uncertainty relation are pursued for time-independent potential whereas average energy and Heisenberg uncertainty relation are defined for time-dependent potential. Forces acting on a fixed boundary wall as well as average force acting on moving boundary wall are presented along various trajectories. For high temperature, analytical forms of partition function and the corresponding thermodynamic quantities are derived following the Euler-Maclaurin summation formula over a finite as well as an infinite domain for accurate presentation. Three quantum systems are generated with the help of point transformation, separation of variables and super-symmetric quantum mechanics from one quantum system and the corresponding results are compared among all systems, where two of them are time-independent and another two are time-dependent.