Approximate Solutions, Thermal Properties and Superstatistics Solutions
to Schr\"odinger Equation
- URL: http://arxiv.org/abs/2110.09896v1
- Date: Sat, 16 Oct 2021 22:02:50 GMT
- Title: Approximate Solutions, Thermal Properties and Superstatistics Solutions
to Schr\"odinger Equation
- Authors: Ituen B. Okon, Clement O. Onate, Ekwevugbe Omugbe, Uduakobong S.
Okorie, Akaninyene D. Antia, Michael C. Onyeaju, Chen Wen-Li, Judith P.Araujo
- Abstract summary: We study thermal properties and superstatistics in terms of partition function (Z) and other thermodynamic properties.
The proposed potential model reduces to Hellmann potential, Yukawa potential, Screened Hyperbolic potential and Coulomb potential as special cases.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: In this work, we apply the parametric Nikiforov-Uvarov method to obtain eigen
solutions and total normalized wave function of Schr\"odinger equation express
in terms of Jacobi polynomial using Coulomb plus Screened Exponential
Hyperbolic potential (CPSEHP), where we obtained the probability density plots
for the proposed potential for various orbital angular quantum number, as well
as some special cases (Hellmann and Yukawa potential).The proposed potential is
best suitable for smaller values of the screening parameter .The resulting
energy eigen equation is presented in a close form and extended to study
thermal properties and superstatistics express in terms of partition function
(Z) and other thermodynamic properties such as; vibrational mean energy (U) ,
vibrational specific heat capacity (C) ,vibrational entropy(S) and vibrational
free energy(F) . Using the resulting energy equation and with the help of
Matlab software, the numerical bound state solutions were obtained for various
values of the screening parameter ( alpha) as well as different expectation
values via Hellmann-Feynman Theorem (HFT). The trend of the partition function
and other thermodynamic properties obtained for both thermal properties and
superstatistics were in excellent agreement with the existing literatures. Due
to the analytical mathematical complexities, the superstatistics and thermal
properties were evaluated using Mathematica 10.0 version software. The proposed
potential model reduces to Hellmann potential, Yukawa potential, Screened
Hyperbolic potential and Coulomb potential as special cases.
Related papers
- Cavity QED materials: Comparison and validation of two linear response theories at arbitrary light-matter coupling strengths [41.94295877935867]
We develop a linear response theory for materials collectively coupled to a cavity that is valid in all regimes of light-matter coupling.
We compare two different approaches to obtain thermal Green functions.
We provide a detailed application of the theory to the Quantum Hall effect and to a collection of magnetic models.
arXiv Detail & Related papers (2024-06-17T18:00:07Z) - The Tempered Hilbert Simplex Distance and Its Application To Non-linear
Embeddings of TEMs [36.135201624191026]
We introduce three different parameterizations of finite discrete TEMs via Legendre functions of the negative tempered entropy function.
Similar to the Hilbert geometry, the tempered Hilbert distance is characterized as a $t$-symmetrization of the oriented tempered Funk distance.
arXiv Detail & Related papers (2023-11-22T15:24:29Z) - Eigen Solution and Thermodynamic Properties of Manning Rosen Plus
Exponential Yukawa Potential [0.0]
We obtained analytical bound state solution of the Schr"odinger equation with Manning Rosen plus Yukawa Potential.
The energy eigen equation was determined and presented in compact form.
arXiv Detail & Related papers (2023-03-21T11:56:32Z) - Ro-vibrational energy and thermodynamic properties of molecules
subjected to Deng-Fan potential through an improved approximation [0.0]
A modified Pekeris-type approximation is proposed for the centrifugal term.
The effect of quantum correction on partition function and thermodynamic properties is discussed.
arXiv Detail & Related papers (2022-05-19T14:32:19Z) - Application of Eckart-Hellmann potential to study selected diatomic
molecules using Nikiforov-Uvarov-Functional Analysis (NUFA) method [0.0]
We study the energy levels of the Schr"odinger equation under the Eckart-Hellmann potential (EHP) energy function.
The numerical bound states energy for various screening parameters at different quantum states and vibrational energies of EHP for CuLi, TiH, VH, and TiC diatomic molecules were computed.
arXiv Detail & Related papers (2022-04-08T19:24:43Z) - Eigensolutions and Thermodynamic Properties of Kratzer plus generalized
Morse Potential [0.0]
We apply the parametric Nikiforov-Uvarov method to obtain the bound state solution of Schrodinger wave equation in the presence of Kratzer plus generalized Morse potential (KPGM)
The resulting energy eigen equation were use to study partition function and other thermodynamic properties such as vibrational mean energy, vibrational specific heat capacity, vibrational mean free energy and vibrational entropy for the proposed potential as applied to lithium hydride diatomic molecule.
arXiv Detail & Related papers (2022-02-19T18:51:32Z) - Uhlmann Fidelity and Fidelity Susceptibility for Integrable Spin Chains
at Finite Temperature: Exact Results [68.8204255655161]
We show that the proper inclusion of the odd parity subspace leads to the enhancement of maximal fidelity susceptibility in the intermediate range of temperatures.
The correct low-temperature behavior is captured by an approximation involving the two lowest many-body energy eigenstates.
arXiv Detail & Related papers (2021-05-11T14:08:02Z) - Exact thermal properties of free-fermionic spin chains [68.8204255655161]
We focus on spin chain models that admit a description in terms of free fermions.
Errors stemming from the ubiquitous approximation are identified in the neighborhood of the critical point at low temperatures.
arXiv Detail & Related papers (2021-03-30T13:15:44Z) - Evolution of a Non-Hermitian Quantum Single-Molecule Junction at
Constant Temperature [62.997667081978825]
We present a theory for describing non-Hermitian quantum systems embedded in constant-temperature environments.
We find that the combined action of probability losses and thermal fluctuations assists quantum transport through the molecular junction.
arXiv Detail & Related papers (2021-01-21T14:33:34Z) - Thermal Properties of Deng-Fan-Eckart Potential model using Poisson
Summation Approach [0.0]
The Deng-Fan-Eckart potential is as good as the Morse potential in studying atomic interaction in diatomic molecules.
The thermodynamic properties of some selected diatomic molecules(H2, CO, and ScN ) were obtained using Poisson summation method.
arXiv Detail & Related papers (2020-09-19T20:15:06Z) - Method of spectral Green functions in driven open quantum dynamics [77.34726150561087]
A novel method based on spectral Green functions is presented for the simulation of driven open quantum dynamics.
The formalism shows remarkable analogies to the use of Green functions in quantum field theory.
The method dramatically reduces computational cost compared with simulations based on solving the full master equation.
arXiv Detail & Related papers (2020-06-04T09:41:08Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.