scholarly journals A new application of the quantum mechanical hypervirial theorems technique

2020 ◽  
Vol 9 ◽  
pp. 210
Author(s):  
M. E. Grypeos ◽  
Th. E. Liolios
Keyword(s):  
Wide Class ◽  
Ground State ◽  
State Energy ◽  
Bound State ◽  
Quantum Mechanical ◽  
Bound State Energy ◽  
New Approach ◽  
Analytic Determination ◽  
Gaussian Potential

A new approach is proposed on the basis of the quantum mechanical hypervirial theorems technique for the approximate analytic (or semi-analytic) determination of bound state energy eigenfunctions for quite a wide class of central potentials. The accuracy of the method is tested for the Gaussian potential and is best for the ground state.

Lower Bound for ppK– Quasi-Bound State Energy

2020 ◽  
Vol 51 (5) ◽  
pp. 979-987 ◽  
Author(s):  
I. Filikhin ◽  
B. Vlahovic
Keyword(s):  
Lower Bound ◽  
State Energy ◽  
Bound State ◽  
Bound State Energy ◽  
Quasi Bound State

Effect of the velocity-dependent potentials on the energy eigenvalues of the Morse potential

Open Physics ◽  
2012 ◽  
Vol 10 (4) ◽  
Author(s):  
Asim Soylu ◽  
Orhan Bayrak ◽  
Ismail Boztosun
Keyword(s):  
Morse Potential ◽  
State Energy ◽  
Bound State ◽  
Quantum States ◽  
Bound State Energy ◽  
Energy Eigenvalues ◽  
Dependent Term ◽  
Oscillator Type ◽  
Dependent Potential ◽  
Pekeris Approximation

AbstractWe investigate the effect of the isotropic velocity-dependent potentials on the bound state energy eigenvalues of the Morse potential for any quantum states. When the velocity-dependent term is used as a constant parameter, ρ(r) = ρ 0, the energy eigenvalues can be obtained analytically by using the Pekeris approximation. When the velocity-dependent term is considered as an harmonic oscillator type, ρ(r) = ρ 0 r 2, we show how to obtain the energy eigenvalues of the Morse potential without any approximation for any n and ℓ quantum states by using numerical calculations. The calculations have been performed for different energy eigenvalues and different numerical values of ρ 0, in order to show the contribution of the velocity-dependent potential on the energy eigenvalues of the Morse potential.

scholarly journals ANY l-STATE ANALYTICAL SOLUTIONS OF THE KLEIN–GORDON EQUATION FOR THE WOODS–SAXON POTENTIAL

2010 ◽  
Vol 19 (07) ◽  
pp. 1463-1475 ◽  
Author(s):  
V. H. BADALOV ◽  
H. I. AHMADOV ◽  
S. V. BADALOV
Keyword(s):  
State Energy ◽  
Gordon Equation ◽  
Bound State ◽  
Nonrelativistic Limit ◽  
Saxon Potential ◽  
Bound State Energy ◽  
Klein Gordon ◽  
Uvarov Method ◽  
Pekeris Approximation ◽  
Klein Gordon Equation

The radial part of the Klein–Gordon equation for the Woods–Saxon potential is solved. In our calculations, we have applied the Nikiforov–Uvarov method by using the Pekeris approximation to the centrifugal potential for any l-states. The exact bound state energy eigenvalues and the corresponding eigenfunctions are obtained on the various values of the quantum numbers n and l. The nonrelativistic limit of the bound state energy spectrum was also found.

scholarly journals EXACT SOLUTION OF THE SCHRÖDINGER EQUATION FOR THE MODIFIED KRATZER'S MOLECULAR POTENTIAL WITH POSITION-DEPENDENT MASS

2008 ◽  
Vol 17 (07) ◽  
pp. 1327-1334 ◽  
Author(s):  
RAMAZÀN SEVER ◽  
CEVDET TEZCAN
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
State Energy ◽  
Bound State ◽  
Bound State Energy ◽  
Energy Eigenvalues ◽  
Molecular Potential ◽  
Dependent Mass ◽  
Morse Potentials ◽  
Position Dependent Mass

Exact solutions of Schrödinger equation are obtained for the modified Kratzer and the corrected Morse potentials with the position-dependent effective mass. The bound state energy eigenvalues and the corresponding eigenfunctions are calculated for any angular momentum for target potentials. Various forms of point canonical transformations are applied.

Thermodynamics and Phase Transitions in Dense Hydrogen - the Role of Bound State Energy Shifts

2008 ◽  
Vol 48 (9-10) ◽  
pp. 670-685 ◽  
Author(s):  
W. Ebeling ◽  
R. Redmer ◽  
H. Reinholz ◽  
G. Röpke
Keyword(s):  
Phase Transitions ◽  
State Energy ◽  
Bound State ◽  
Bound State Energy

Analytical solutions of fractional Schrödinger equation and thermal properties of Morse potential for some diatomic molecules

2021 ◽  
pp. 2150041
Author(s):  
U. S. Okorie ◽  
A. N. Ikot ◽  
G. J. Rampho ◽  
P. O. Amadi ◽  
Hewa Y. Abdullah
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Morse Potential ◽  
State Energy ◽  
Diatomic Molecules ◽  
Bound State ◽  
Bound State Energy ◽  
Fractional Schrödinger Equation ◽  
Energy Eigenvalues ◽  
Fractional Schrodinger Equation

By employing the concept of conformable fractional Nikiforov–Uvarov (NU) method, we solved the fractional Schrödinger equation with the Morse potential in one dimension. The analytical expressions of the bound state energy eigenvalues and eigenfunctions for the Morse potential were obtained. Numerical results for the energies of Morse potential for the selected diatomic molecules were computed for different fractional parameters chosen arbitrarily. Also, the graphical variation of the bound state energy eigenvalues of the Morse potential for hydrogen dimer with vibrational quantum number and the range of the potential were discussed, with regards to the selected fractional parameters. The vibrational partition function and other thermodynamic properties such as vibrational internal energy, vibrational free energy, vibrational entropy and vibrational specific heat capacity were evaluated in terms of temperature. Our results are new and have not been reported in any literature before.

EXACT SOLUTIONS OF DIRAC EQUATION FOR A NEW SPHERICALLY ASYMMETRICAL SINGULAR OSCILLATOR

2010 ◽  
Vol 25 (33) ◽  
pp. 2849-2857 ◽  
Author(s):  
GUO-HUA SUN ◽  
SHI-HAI DONG
Keyword(s):  
Dirac Equation ◽  
Vector Potential ◽  
State Energy ◽  
Energy Levels ◽  
Scalar Potential ◽  
Bound State ◽  
Wave Functions ◽  
Bound State Energy ◽  
Exact Bound ◽  
Spinor Wave

In this work we solve the Dirac equation by constructing the exact bound state solutions for a mixing of scalar and vector spherically asymmetrical singular oscillators. This is done provided that the vector potential is equal to the scalar potential. The spinor wave functions and bound state energy levels are presented. The case V(r) = -S(r) is also considered.

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