scholarly journals Relativistic Treatment of Quantum Mechanical Gravitational-Harmonic Oscillator Potential

2021 ◽  
Vol 3 (3) ◽  
pp. 42-47
Author(s):  
E. P. Inyang ◽  
B. I. Ita ◽  
E. P. Inyang
Keyword(s):  
Harmonic Oscillator ◽  
Laguerre Polynomials ◽  
Bound State ◽  
Quantum Mechanical ◽  
S Wave ◽  
Oscillator Potential ◽  
Harmonic Oscillator Potential ◽  
Klein Gordon ◽  
Uvarov Method ◽  
Equal Scalar

The solutions of the Klein- Gordon equation for the quantum mechanical gravitational plus harmonic oscillator potential with equal scalar and vector potential have been presented using the parametric Nikiforov-Uvarov method. The energy eigenvalues were obtained in relativistic and non-relativistic regime and the corresponding un-normalized eigenfunctions in terms of Laguerre polynomials. The numerical values for the S – wave bound state were obtained.

EXACT SOLUTIONS OF THE KLEIN–GORDON EQUATION FOR THE ROSEN–MORSE TYPE POTENTIALS VIA NIKIFOROV–UVAROV METHOD

2008 ◽  
Vol 23 (35) ◽  
pp. 3005-3013 ◽  
Author(s):  
A. REZAEI AKBARIEH ◽  
H. MOTAVALI
Keyword(s):  
Exact Solutions ◽  
Gordon Equation ◽  
Bound State ◽  
S Wave ◽  
Vector Potentials ◽  
Klein Gordon ◽  
The One ◽  
Uvarov Method ◽  
Equal Scalar ◽  
Klein Gordon Equation

The exact solutions of the one-dimensional Klein–Gordon equation for the Rosen–Morse type potential with equal scalar and vector potentials are presented. First, we briefly review Nikiforov–Uvarov mathematical method. Using this method, wave functions and corresponding exact energy equation are obtained for the s-wave bound state. It has been shown that the results for Rosen–Morse type potentials reduce to the standard Rosen–Morse well and Eckart potentials in the special case. The PT-symmetry for these potentials is also considered.

scholarly journals Exact Solutions of the Mass-Dependent Klein-Gordon Equation with the Vector Quark-Antiquark Interaction and Harmonic Oscillator Potential

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
M. K. Bahar ◽  
F. Yasuk
Keyword(s):  
Harmonic Oscillator ◽  
Exact Solutions ◽  
Gordon Equation ◽  
Oscillator Potential ◽  
Ansatz Method ◽  
Harmonic Oscillator Potential ◽  
Klein Gordon ◽  
Dependent Mass ◽  
Mass Dependent ◽  
Klein Gordon Equation

Using the asymptotic iteration and wave function ansatz method, we present exact solutions of the Klein-Gordon equation for the quark-antiquark interaction and harmonic oscillator potential in the case of the position-dependent mass.

scholarly journals NEW FEATURES IN SUPERSYMMETRY BREAKDOWN IN QUANTUM MECHANICS

1996 ◽  
Vol 11 (19) ◽  
pp. 1563-1567 ◽  
Author(s):  
BORIS F. SAMSONOV
Keyword(s):  
Quantum Mechanics ◽  
Harmonic Oscillator ◽  
Mechanical Model ◽  
State Energy ◽  
Vacuum State ◽  
Quantum Mechanical ◽  
Oscillator Potential ◽  
Harmonic Oscillator Potential ◽  
Quantum Mechanical Model ◽  
Higher Derivative

The supersymmetric quantum mechanical model based on higher-derivative supercharge operators possessing unbroken supersymmetry and discrete energies below the vacuum state energy is described. As an example harmonic oscillator potential is considered.

SUPERSYMMETRY AND ACCIDENTAL DEGENERACY

1987 ◽  
Vol 02 (06) ◽  
pp. 391-395 ◽  
Author(s):  
P. CELKA ◽  
V. HUSSIN
Keyword(s):  
Harmonic Oscillator ◽  
Three Dimensional ◽  
Quantum Mechanical ◽  
General Context ◽  
Supersymmetric Model ◽  
Oscillator Potential ◽  
Harmonic Oscillator Potential ◽  
Accidental Degeneracy ◽  
Model Hamiltonians

Accidental degeneracies are explained as arising from an underlying supersymmetry associated with the superalgebra osp (2/2, ℝ)⊕ so (3) when the quantum-mechanical potential is a general superposition of a three-dimensional harmonic oscillator potential, a 1/r2-potential and a constant one. Recent supersymmetric model hamiltonians are discussed within our general context.

BOUND STATE SOLUTIONS OF THE DIRAC EQUATION FOR THE SCARF-TYPE POTENTIAL USING NIKIFOROV–UVAROV METHOD

2009 ◽  
Vol 24 (15) ◽  
pp. 1227-1236 ◽  
Author(s):  
HOSSEIN MOTAVALI
Keyword(s):  
Dirac Equation ◽  
Bound State ◽  
S Wave ◽  
Spinor Wave Function ◽  
Vector Potentials ◽  
Special Cases ◽  
The One ◽  
Uvarov Method ◽  
Equal Scalar ◽  
Type Potential

In this paper we present the analytical solutions of the one-dimensional Dirac equation for the Scarf-type potential with equal scalar and vector potentials. Using Nikiforov–Uvarov mathematical method, spinor wave function and the corresponding exact energy equation are obtained for the s-wave bound state. It has been shown that the results for this potential reduce to the well-known potentials in the special cases.

EXACT SOLUTIONS OF THE SCHRÖDINGER EQUATION FOR A NEW RING-SHAPED NONHARMONIC OSCILLATOR POTENTIAL

2008 ◽  
Vol 23 (12) ◽  
pp. 1919-1927 ◽  
Author(s):  
YAN-FU CHENG ◽  
TONG-QING DAI
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Laguerre Polynomials ◽  
Bound State ◽  
Wave Functions ◽  
Oscillator Potential ◽  
Radial Wave ◽  
Generalized Laguerre Polynomials ◽  
Uvarov Method ◽  
Special Case

The bound state solutions of the Schrödinger equation with a new ring-shaped nonharmonic potential are presented using exactly the Nikiforov–Uvarov method. It is found that the solutions of the angular wave function can be expressed by Jacobi polynomial and radial wave functions are given by the generalized Laguerre polynomials. We also discuss the special case for α = 0 and β = 0 respectively.

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.

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