Extension of perturbation theory to quantum systems with conformable derivative

2021 ◽  
Author(s):  
Mohamed Al-Masaeed ◽  
Eqab M Rabei ◽  
Ahmed Al-Jamel ◽  
Dumitru Baleanu
Keyword(s):  
Perturbation Theory ◽  
Quantum Mechanics ◽  
Hamiltonian Systems ◽  
Quantum Systems ◽  
Traditional Theory ◽  
Conformable Derivative ◽  
Eigenvalues And Eigenfunctions ◽  
Energy Eigenvalues ◽  
Standard Values ◽  
Energy Eigenvalues And Eigenfunctions

In this paper, the perturbation theory is extended to be applicable for systems containing conformable derivative of fractional order [Formula: see text]. This is needed as an essential and powerful approximation method for describing systems with conformable differential equations that are difficult to solve analytically. The work here is derived and discussed for the conformable Hamiltonian systems that appears in the conformable quantum mechanics. The required [Formula: see text]-corrections for the energy eigenvalues and eigenfunctions are derived. To demonstrate this extension, three illustrative examples are given, and the standard values obtained by the traditional theory are recovered when [Formula: see text].

scholarly journals EIGENVALUES AND EIGENFUNCTIONS OF WOODS–SAXON POTENTIAL IN PT-SYMMETRIC QUANTUM MECHANICS

2006 ◽  
Vol 21 (27) ◽  
pp. 2087-2097 ◽  
Author(s):  
AYŞE BERKDEMIR ◽  
CÜNEYT BERKDEMIR ◽  
RAMAZAN SEVER
Keyword(s):  
Quantum Mechanics ◽  
Real Spectrum ◽  
Saxon Potential ◽  
Eigenvalues And Eigenfunctions ◽  
Discrete Energy ◽  
Energy Eigenvalues ◽  
Symmetric Quantum ◽  
Symmetric Version ◽  
Uvarov Method ◽  
S States

Using the Nikiforov–Uvarov method which is based on solving the second-order differential equations, we firstly analyzed the energy spectra and eigenfunctions of the Woods–Saxon potential. In the framework of the PT-symmetric quantum mechanics, we secondly solved the time-independent Schrödinger equation for the PT and non-PT-symmetric version of the potential. It is shown that the discrete energy eigenvalues of the non-PT-symmetric potential consist of the real and imaginary parts, but the PT-symmetric one has a real spectrum. Results are obtained for s-states only.

Exactly separable Bohr Hamiltonian with the Morse potential for triaxial nuclei

2014 ◽  
Vol 23 (10) ◽  
pp. 1450053 ◽  
Author(s):  
I. Inci
Keyword(s):  
Experimental Data ◽  
Closed Form ◽  
Morse Potential ◽  
Electric Quadrupole ◽  
Quadrupole Transition ◽  
Eigenvalues And Eigenfunctions ◽  
Energy Eigenvalues ◽  
Electric Quadrupole Transition ◽  
Energy Eigenvalues And Eigenfunctions

In this paper, the Morse potential is used in the β-part of the collective Bohr Hamiltonian for triaxial nuclei. Energy eigenvalues and eigenfunctions are obtained in a closed form through exactly separating the Hamiltonian into its variables by using an appropriate form of the potential. The results are applied to generate the nuclear spectrum of 192 Pt , 194 Pt and 196 Pt isotopes which are known to be the best candidate exhibiting triaxiality. Electric quadrupole transition ratios are calculated and then compared with the experimental data and the Z(5) model results.

scholarly journals Analytical solution of energy eigen value, eigen function and angular wave function of Dirac equation with Rosen Morse plus Rosen Morse potential in terms of Romanovski polynomials for exact spin symmetry

2017 ◽  
Vol 1 (1) ◽  
pp. 1
Author(s):  
Ihtiari Prasetyaningrum ◽  
C Cari ◽  
A Suparmi
Keyword(s):  
Dirac Equation ◽  
Morse Potential ◽  
State Energy ◽  
Spin Symmetry ◽  
Bound State ◽  
Bound State Energy ◽  
Eigenvalues And Eigenfunctions ◽  
Energy Eigenvalues ◽  
Eigen Value ◽  
Energy Eigenvalues And Eigenfunctions

<p class="Abstract">The energy eigenvalues and eigenfunctions of Dirac equation for Rosen Morse plus Rosen Morse potential are investigated numerically in terms of finite Romanovsky Polynomial. The bound state energy eigenvalues are given in a closed form and corresponding eigenfunctions are obtained in terms of Romanovski polynomials. The energi eigen value is solved by numerical method with Matlab 2011.</p>

Analytical solution of energy eigen value, eigen function and angular wave function of Dirac equation with Rosen Morse plus Rosen Morse potential in terms of Romanovski polynomials for exact spin symmetry

2017 ◽  
Vol 1 (1) ◽  
pp. 1
Author(s):  
Ihtiari Prasetyaningrum ◽  
C Cari ◽  
A Suparmi
Keyword(s):  
Dirac Equation ◽  
Morse Potential ◽  
State Energy ◽  
Spin Symmetry ◽  
Bound State ◽  
Bound State Energy ◽  
Eigenvalues And Eigenfunctions ◽  
Energy Eigenvalues ◽  
Eigen Value ◽  
Energy Eigenvalues And Eigenfunctions

<p class="Abstract">The energy eigenvalues and eigenfunctions of Dirac equation for Rosen Morse plus Rosen Morse potential are investigated numerically in terms of finite Romanovsky Polynomial. The bound state energy eigenvalues are given in a closed form and corresponding eigenfunctions are obtained in terms of Romanovski polynomials. The energi eigen value is solved by numerical method with Matlab 2011.</p>

Single-centre expansions for the hydrogen molecular ion. II

1962 ◽  
Vol 58 (1) ◽  
pp. 130-135 ◽  
Author(s):  
M. Cohen
Keyword(s):  
Ground State ◽  
State Energy ◽  
Internuclear Separation ◽  
Single Centre ◽  
Eigenvalues And Eigenfunctions ◽  
Exact Wave Function ◽  
Radial Functions ◽  
Energy Eigenvalues ◽  
Energy Eigenvalues And Eigenfunctions ◽  
Good Agreement

In an earlier paper (Cohen and Coulson(3), referred to hereafter as I), it was shown that satisfactory energy eigenvalues and eigenfunctions for various even σ-states of may be obtained using a single-centre expansion, provided that the radial functions are properly determined. In particular, the ground-state energy at the equilibrium internuclear separation of 2 a.u. was found to be within 0·25% of the exact value (Bates, Ledsham and Stewart (2)), and the eigenfunction reproduced all the characteristics of the exact wave-function. The method has now been extended to the odd σ-states, as well as to the two lowest π-states (2pπu, 3dπg), and the results are in good agreement with the calculations of Bates et al.

scholarly journals Intensity-dependent nonlinear optical properties in an asymmetric Gaussian potential quantum well modulated by external fields

2021 ◽  
Author(s):  
Muhammed Sayraç ◽  
Aslan Turkoglu ◽  
Miguel Eduvardo Mora-Ramos ◽  
fatih ungan
Keyword(s):  
Quantum Well ◽  
Nonlinear Optical ◽  
Optical Rectification ◽  
External Fields ◽  
Eigenvalues And Eigenfunctions ◽  
Third Harmonic ◽  
Gaussian Potential ◽  
Energy Eigenvalues ◽  
Energy Eigenvalues And Eigenfunctions ◽  
Nonlinear Optical Rectification

Abstract In this paper, the effects of external electric, magnetic and non-resonant intense laser fields on the nonlinear optical rectification (NOR), second-harmonic (SH), and third-harmonic (TH) generation in a GaAs quantum well with asymmetrical Gaussian potential are theoretically investigated. Firstly, the energy eigenvalues and eigenfunctions of a single electron confined in the structure are obtained by using the diagonalization method within the framework of the effective-mass and parabolic band approaches. Then, using these energy eigenvalues and eigenfunctions, expressions derived within the compact density matrix approximation has been employed to calculate the coefficients of the nonlinear optical response in the structure. The obtained simulation results show that the influence of the external fields leads to significant changes in the coefficients of nonlinear optical rectification, second and third harmonic generation in the system. As a result, it has been seen that the amplitude and position of the peaks of nonlinear optical rectification, second and third harmonic coefficients can be controlled by changing the applied external fields.

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