Two exactly solvable models for the collapse of the particle to the center in a nonrelativistic quantum mechanics

1984 ◽  
Vol 40 (5) ◽  
pp. 145-146 ◽  
Author(s):  
A. A. Berezin
Keyword(s):  
Quantum Mechanics ◽  
Exactly Solvable Models ◽  
Solvable Models ◽  
Nonrelativistic Quantum ◽  
Exactly Solvable ◽  
Nonrelativistic Quantum Mechanics

LIE-ALGEBRAIC APPROACH TO THE PROBLEM OF QUASI-EXACT SOLUBILITY IN QUANTUM MECHANICS

1990 ◽  
Vol 05 (23) ◽  
pp. 1891-1899 ◽  
Author(s):  
A. G. USHVERIDZE
Keyword(s):  
Quantum Mechanics ◽  
Lie Algebras ◽  
Algebraic Approach ◽  
New Method ◽  
Exactly Solvable Models ◽  
Solvable Models ◽  
Simple Lie Algebras ◽  
Infinite Dimensional ◽  
Exactly Solvable

A new method of constructing quasi-exactly solvable models of quantum mechanics is proposed. This method is based on the use of infinite-dimensional representations of simple and semi-simple Lie algebras.

QUASI-EXACTLY SOLVABLE MULTI-DIMENSIONAL SCHRÖDINGER EQUATIONS

1991 ◽  
Vol 06 (11) ◽  
pp. 977-979 ◽  
Author(s):  
A.G. USHVERIDZE
Keyword(s):  
Quantum Mechanics ◽  
New Method ◽  
Schrodinger Equations ◽  
Exactly Solvable Models ◽  
Schrödinger Equations ◽  
Solvable Models ◽  
Exactly Solvable

A new method of constructing multi-dimensional quasi-exactly solvable models of quantum mechanics is proposed.

scholarly journals Dirac Equation in the Presence of Hartmann and Ring-Shaped Oscillator Potentials

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Zahra Bakhshi
Keyword(s):  
Quantum Mechanics ◽  
Energy Spectrum ◽  
Dirac Equation ◽  
Bound States ◽  
Scalar Potential ◽  
Solvable Models ◽  
Nonrelativistic Quantum ◽  
Physical Conditions ◽  
Basic Model ◽  
Nonrelativistic Quantum Mechanics

The importance of the energy spectrum of bound states and their restrictions in quantum mechanics due to the different methods have been used for calculating and determining the limit of them. Comparison of Schrödinger-like equation obtained by Dirac equation with the nonrelativistic solvable models is the most efficient method. By this technique, the exact relativistic solutions of Dirac equation for Hartmann and Ring-Shaped Oscillator Potentials are accessible, when the scalar potential is equal to the vector potential. Using solvable nonrelativistic quantum mechanics systems as a basic model and considering the physical conditions provide the changes in the restrictions of relativistic parameters based on the nonrelativistic definitions of parameters.

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