Exact solutions for the potential V(r) = r2 + β/r4 + λ/r6 by supersymmetric quantum mechanics

1995 ◽  
Vol 73 (7-8) ◽  
pp. 519-525 ◽  
Author(s):  
Y. P. Varshni ◽  
Nivedita Nag ◽  
Rajkumar Roychoudhury
Keyword(s):  
Quantum Mechanics ◽  
Exact Solutions ◽  
Excited States ◽  
Ground State ◽  
Supersymmetric Quantum Mechanics

A method based on supersymmetric quantum mechanics is given for obtaining exact solutions of the potential V(r) = r2 + β/r4 + λ/r6, where β and λ are parameters, provided a certain constraint is satisfied between β and λ. Detailed results are given for the ground state as well as for several excited states. A method for determining the exact energies of two levels for the same values of β and λ is given and illustrated by examples.

Calculation of energy eigenvalues via supersymmetric quantum mechanics

1989 ◽  
Vol 67 (10) ◽  
pp. 931-934 ◽  
Author(s):  
Francisco M. Fernández ◽  
Q. Ma ◽  
D. J. DeSmet ◽  
R. H. Tipping
Keyword(s):  
Quantum Mechanics ◽  
Ground State ◽  
Potential Energy Function ◽  
Supersymmetric Quantum Mechanics ◽  
Energy Eigenvalues ◽  
Arbitrary Power ◽  
Rational Function Approximation ◽  
Ricatti Equation ◽  
Original Potential ◽  
Ground State Energies

A systematic procedure using supersymmetric quantum mechanics is presented for calculating the energy eigenvalues of the Schrödinger equation. Starting from the Hamiltonian for a given potential-energy function, a sequence of supersymmetric partners is derived such that the ground-state energy of the kth one corresponds to the kth eigen energy of the original potential. Various theoretical procedures for obtaining ground-state energies, including a method involving a rational-function approximation for the solution of the Ricatti equation that is outlined in the present paper, can then be applied. Illustrative numerical results for two one-dimensional parity-invariant model potentials are given, and the results of the present procedure are compared with those obtainable via other methods. Generalizations of the method for arbitrary power-law potentials and for radial problems are discussed briefly.

Exact Solutions of Two Body Dirac Equations

1994 ◽  
Vol 49 (10) ◽  
pp. 983-986
Author(s):  
Nivedita Nag ◽  
Rajkumar Roychoudhury
Keyword(s):  
Quantum Mechanics ◽  
Exact Solutions ◽  
Supersymmetric Quantum Mechanics ◽  
Dirac Equations ◽  
Eigen Values

Abstract A set of exact eigen values and eigen functions for the two body Dirac problem described by the Hamiltonian H = (α⃗1 - α⃗2)p⃗ + β1m 1+ β2m2 + ½ (β1 + β2) λrare obtained using the properties of Supersymmetric Quantum Mechanics.

ALGEBRAIC APPROACH TO THE KLEIN–GORDON EQUATION WITH HYPERBOLIC SCARF POTENTIAL

2011 ◽  
Vol 20 (01) ◽  
pp. 55-61 ◽  
Author(s):  
SHISHAN DONG ◽  
SHI-HAI DONG ◽  
H. BAHLOULI ◽  
V. B. BEZERRA
Keyword(s):  
Quantum Mechanics ◽  
Exact Solutions ◽  
Gordon Equation ◽  
Algebraic Approach ◽  
Supersymmetric Quantum Mechanics ◽  
Shape Invariance ◽  
One Dimensional ◽  
Scarf Potential ◽  
Klein Gordon ◽  
Klein Gordon Equation

Using the shape invariance approach we obtain exact solutions of one-dimensional Klein–Gordon equation with equal types of scalar and vector hyperbolic Scarf potentials. This is considered in the framework of supersymmetric quantum mechanics method.

Exact solutions of the Fokker–Planck equation from an nth order supersymmetric quantum mechanics approach

2009 ◽  
Vol 373 (18-19) ◽  
pp. 1610-1615 ◽  
Author(s):  
Axel Schulze-Halberg ◽  
Jesús Morales Rivas ◽  
José Juan Peña Gil ◽  
Jesús García-Ravelo ◽  
Pinaki Roy
Keyword(s):  
Quantum Mechanics ◽  
Exact Solutions ◽  
Planck Equation ◽  
Supersymmetric Quantum Mechanics ◽  
Fokker Planck Equation ◽  
Fokker Planck
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