Nonrelativistic Solutions of Schrodinger Equation and Thermodynamic Properties with the Proposed Modified Mobius Square Plus Eckart Potential

2021 ◽  
Author(s):  
Chibueze P. Onyenegecha ◽  
Ifeanyi J. Njoku ◽  
Alex I. Opara ◽  
Obi Kingsley Echendu ◽  
Ejiro N. Omokoro ◽  
...  
Keyword(s):  
Thermodynamic Properties ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Eckart Potential

ARBITRARY l-WAVE BOUND STATE SOLUTIONS OF THE SCHRÖDINGER EQUATION WITH THE ECKART POTENTIAL

2009 ◽  
Vol 23 (18) ◽  
pp. 2269-2279 ◽  
Author(s):  
YONG-FENG DIAO ◽  
LIANG-ZHONG YI ◽  
TAO CHEN ◽  
CHUN-SHENG JIA
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Approximation Scheme ◽  
Function Analysis ◽  
Bound State ◽  
Centrifugal Term ◽  
Radial Wave ◽  
Shape Invariance ◽  
Eckart Potential ◽  
Analytical Results

By using a modified approximation scheme to deal with the centrifugal term, we solve approximately the Schrödinger equation for the Eckart potential with the arbitrary angular momentum states. The bound state energy eigenvalues and the unnormalized radial wave functions are approximately obtained in a closed form by using the supersymmetric shape invariance approach and the function analysis method. The numerical experiments show that our analytical results are in better agreement with those obtained by using the numerical integration approach than the analytical results obtained by using the conventional approximation scheme to deal with the centrifugal term.

Any ℓ-state solutions of the Eckart potential via asymptotic iteration method

Open Physics ◽  
2012 ◽  
Vol 10 (4) ◽  
Author(s):  
Babatunde Falaye
Keyword(s):  
Schrödinger Equation ◽  
Excellent Agreement ◽  
Iteration Method ◽  
Schrodinger Equation ◽  
Asymptotic Iteration Method ◽  
Centrifugal Term ◽  
Energy Eigenvalues ◽  
Eckart Potential ◽  
Term Energy

AbstractThe asymptotic iteration method is employed to calculate the any ℓ-state solutions of the Schrödinger equation with the Eckart potential by proper approximation of the centrifugal term. Energy eigenvalues and corresponding eigenfunctions are obtain explicitly. The energy eigenvalues are calculated numerically for some values of ℓ and n. Our results are in excellent agreement with the findings of other methods for short potential ranges.

Superstatistics and canonical quantization of the damped harmonic oscillator

2019 ◽  
Vol 34 (14) ◽  
pp. 1950108 ◽  
Author(s):  
S. Sargolzaeipor ◽  
H. Hassanabadi ◽  
W. S. Chung
Keyword(s):  
Thermodynamic Properties ◽  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Schrodinger Equation ◽  
Canonical Quantization ◽  
Quantization Method ◽  
Dirac Delta ◽  
Energy Eigenvalues ◽  
Damped Harmonic Oscillator ◽  
Gamma Distributions

In this paper, we investigate the behavior of the energy eigenvalues of the Schrödinger equation by using the canonical quantization method. We obtain the Hamiltonian of the Schrödinger equation by the Lagrangian in terms of the new coordinates. Then we calculate the partition function by the eigenvalues and the thermodynamic properties of the system in the superstatistics formalism for the modified Dirac delta and the Gamma distributions. All results in the limiting cases satisfy that of the harmonic oscillator. Furthermore, the effects of the all parameters in the problem of energy eigenvalues and thermodynamic properties are calculated and shown graphically.

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