scholarly journals Exact quantization rule and the invariant

2006 ◽  
Vol 55 (4) ◽  
pp. 1571
Author(s):  
Ma Zhong-Qi ◽  
Xu Bo-Wei
Keyword(s):  
Quantization Rule ◽  
Exact Quantization Rule

scholarly journals Approximate analytical solutions for arbitrary l-state of the Hulthén potential with an improved approximation of the centrifugal term

2011 ◽  
Vol 9 (4) ◽  
pp. 737-742 ◽  
Author(s):  
Jerzy Stanek
Keyword(s):  
Bound State ◽  
Centrifugal Term ◽  
Approximate Methods ◽  
Quantization Rule ◽  
Hulthén Potential ◽  
Hulthen Potential ◽  
Approximate Analytical Solutions ◽  
Exact Quantization Rule ◽  
Screening Parameter ◽  
Uvarov Method

AbstractAn approximate analytical solution of the radial Schrödinger equation for the generalized Hulthén potential is obtained by applying an improved approximation of the centrifugal term. The bound state energy eigenvalues and the normalized eigenfunctions are given in terms of hypergeometric polynomials. The results for arbitrary quantum numbers n r and l with different values of the screening parameter δ are compared with those obtained by the numerical method, asymptotic iteration, the Nikiforov-Uvarov method, the exact quantization rule, and variational methods. The results obtained by the method proposed in this work are in a good agreement with those obtained by other approximate methods.

scholarly journals ROTATIONAL-VIBRATIONAL EIGEN SOLUTIONS OF THE D-DIMENSIONAL SCHRÖDINGER EQUATION FOR THE IMPROVED WEI POTENTIAL

2020 ◽  
Vol 4 (2) ◽  
pp. 269-283
Author(s):  
Edwin Samson Eyube ◽  
Yabwa Dlama ◽  
Umar Wadata
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Goodness Of Fit ◽  
Bound State ◽  
Fit Indices ◽  
Quantization Rule ◽  
Exact Quantization Rule ◽  
Vibrational Energies ◽  
Eigen Solutions ◽  
Tietz Potential

In this present study, we have employed the techniques of exact quantization rule and ansatz solution method to obtain closed form expressions for the rotational-vibrational eigensolutions of the D-dimensional Schrödinger equation for the improved Wei potential, for cases of h′ ≠ 0 and h′ = 0. By using our derived energy equation and choosing arbitrary values of n and ℓ, we have computed the bound state rotational-vibrational energies of CO, H2 and LiH for various quantum states. The mean absolute percentage deviation (MAPD) and the Lippincott criterion ware used as a goodness-of-fit indices to compare our result with the Rydberg-Klein-Rees (RKR) and improved Tietz potential data in the literature. MAPD of 0.2862%, 0.2896% and 0.0662% relative to the RKR data for CO ware obtained. For the improved Wei and Morse potential, our computed energy eigenvalues for CO, H2 and LiH are in excellent agreement with existing results in the literature

EXACT QUANTIZATION RULE AND ITS APPLICATIONS TO PHYSICAL POTENTIALS

2007 ◽  
Vol 16 (01) ◽  
pp. 189-198 ◽  
Author(s):  
SHI-HAI DONG ◽  
D. MORALES ◽  
J. GARCÍA-RAVELO
Keyword(s):  
Harmonic Oscillator ◽  
Analytical Solutions ◽  
Bound States ◽  
Energy Levels ◽  
Present Approach ◽  
Three Dimensions ◽  
One Dimension ◽  
Quantization Rule ◽  
Exact Quantization Rule ◽  
Pseudoharmonic Oscillator

By using the exact quantization rule, we present analytical solutions of the Schrödinger equation for the deformed harmonic oscillator in one dimension, the Kratzer potential and pseudoharmonic oscillator in three dimensions. The energy levels of all the bound states are easily calculated from this quantization rule. The normalized wavefunctions are also obtained. It is found that the present approach can simplify the calculations.

Application of the exact quantization rule for some noncentral separable potentials

2008 ◽  
Vol 86 (9) ◽  
pp. 1083-1089 ◽  
Author(s):  
Y Kasri ◽  
L Chetouani
Keyword(s):  
Energy Spectrum ◽  
Quantization Rule ◽  
Exact Quantization Rule ◽  
Separable Potentials ◽  
03.65 Ge

The energy spectrum of some noncentral separable potentials are obtained using the exact quantization rule in r and θ dimensions. The results are consistent with those obtained by other methods. PACS Nos.: 03.65.Ca, 03.65.Ge

scholarly journals EXACT QUANTIZATION RULES FOR BOUND STATES OF THE SCHRÖDINGER EQUATION

2005 ◽  
Vol 14 (04) ◽  
pp. 599-610 ◽  
Author(s):  
ZHONG-QI MA ◽  
BO-WEI XU
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Bound States ◽  
Three Dimensional ◽  
Spherically Symmetric ◽  
Quantization Rule ◽  
One Dimensional ◽  
Exact Quantization Rule ◽  
The One ◽  
Quantization Rules

An exact quantization rule for the bound states of the one-dimensional Schrödinger equation is presented and is generalized to the three-dimensional Schrödinger equation with a spherically symmetric potential.

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