scholarly journals Exactly Solvable Problems in Quantum Mechanics

2020 ◽  
Author(s):  
Lourdhu Bruno Chandrasekar ◽  
Kanagasabapathi Gnanasekar ◽  
Marimuthu Karunakaran
Keyword(s):  
Quantum Mechanics ◽  
Exactly Solvable ◽  
Solvable Problems

Exactly solvable problems of quantum mechanics and their spectrum generating algebras: A review

Open Physics ◽  
2007 ◽  
Vol 5 (2) ◽  
Author(s):  
Constantin Rasinariu ◽  
Jeffry Mallow ◽  
Asim Gangopadhyaya
Keyword(s):  
Quantum Mechanics ◽  
Shape Invariance ◽  
Exactly Solvable ◽  
Solvable Problems ◽  
Made In

AbstractIn this review, we summarize the progress that has been made in connecting supersymmetry and spectrum generating algebras through the property of shape invariance. This monograph is designed to be used by our fellow researchers, by other interested physicists, and by students at the graduate and even undergraduate levels who would like a brief introduction to the field.

SUPERSYMMETRIC QUANTUM MECHANICS AND PARTIAL ALGEBRAIZATION OF THE SPECTRAL PROBLEM

1989 ◽  
Vol 04 (13) ◽  
pp. 3305-3310 ◽  
Author(s):  
M.A. SHIFMAN
Keyword(s):  
Quantum Mechanics ◽  
Spectral Problem ◽  
Supersymmetric Quantum Mechanics ◽  
Exactly Solvable ◽  
Solvable Problems

It is shown how Witten’s supersymmetric quantum mechanics can be used to expand the class of quasi-exactly-solvable problems discovered recently.

scholarly journals MULTIDIMENSIONAL EXACTLY SOLVABLE PROBLEMS IN QUANTUM MECHANICS AND PULLBACKS OF AFFINE COORDINATES ON THE GRASSMANNIAN

1992 ◽  
Vol 07 (07) ◽  
pp. 1449-1465 ◽  
Author(s):  
A. LOSEV ◽  
A. TURBINER
Keyword(s):  
Quantum Mechanics ◽  
Scalar Curvature ◽  
Homogeneous Space ◽  
Simple Form ◽  
Symmetry Groups ◽  
Natural Coordinates ◽  
Quadratic Polynomials ◽  
Hidden Symmetry ◽  
Exactly Solvable ◽  
Solvable Problems

Multidimensional exactly solvable problems related to compact hidden-symmetry groups are discussed. Natural coordinates on homogeneous space are introduced. It is shown that a potential and scalar curvature of the problem considered have quite a simple form of quadratic polynomials in these coordinates. A mysterious relation between the potential and the curvature observed for SU(2) in Refs. 2 and 3 is obtained in a simple way.

ON QUASI-EXACTLY SOLVABLE PROBLEMS AND SUPERSYMMETRY

1991 ◽  
Vol 06 (14) ◽  
pp. 1257-1260 ◽  
Author(s):  
P. ROY ◽  
Y.P. VARSHNI
Keyword(s):  
Quantum Mechanics ◽  
Supersymmetric Quantum Mechanics ◽  
Exactly Solvable ◽  
Solvable Problems

We discuss the possibility of obtaining new quasi-exactly solvable systems within the framework of supersymmetric quantum mechanics.

scholarly journals SUSUSY Quantum Mechanics

1997 ◽  
Vol 12 (01) ◽  
pp. 171-176 ◽  
Author(s):  
David J. Fernández C.
Keyword(s):  
Quantum Mechanics ◽  
Shift Operator ◽  
Second Order ◽  
Parametric Family ◽  
First Order ◽  
Shift Operators ◽  
Exactly Solvable ◽  
Exactly Solvable Hamiltonians

The exactly solvable eigenproblems in Schrödinger quantum mechanics typically involve the differential "shift operators". In the standard supersymmetric (SUSY) case, the shift operator turns out to be of first order. In this work, I discuss a technique to generate exactly solvable eigenproblems by using second order shift operators. The links between this method and SUSY are analysed. As an example, we show the existence of a two-parametric family of exactly solvable Hamiltonians, which contains the Abraham–Moses potentials as a particular case.

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