Shape Invariance And Its Connection To Potential Algebra, Asim Gangopadhyaya, Jeffrey Mallow, Uday Sukhatme
Jan 2016
Shape Invariance And Its Connection To Potential Algebra, Asim Gangopadhyaya, Jeffrey Mallow, Uday Sukhatme
Asim Gangopadhyaya
Exactly solvable potentials of nonrelativistic quantum mechanics are known to be shape invariant. For these potentials, eigenvalues and eigenvectors can be derived using well known methods of supersymmetric quantum mechanics. The majority of these potentials have also been shown to possess a potential algebra, and hence are also solvable by group theoretical techniques. In this paper, for a subset of solvable problems, we establish a connection between the two methods and show that they are indeed equivalent.
Generating Shape Invariant Potentials, Asim Gangopadhyaya
Dec 2007
Generating Shape Invariant Potentials, Asim Gangopadhyaya
Asim Gangopadhyaya
We transform the shape invariance condition, a difference-differential equation of supersymmetric quantum mechanics, into a local partial differential equation. We develop a new method for generating translationally shape invariant potentials from this equation. We generate precisely all the known shape invariant potentials, and argue that there are unlikely to be others.
Thermodynamics Of A Free Q Fermion Gas, Asim Gangopadhyaya
Dec 1993
Thermodynamics Of A Free Q Fermion Gas, Asim Gangopadhyaya
Asim Gangopadhyaya
We study the thermodynamics of a q-fermion gas for complex values of q on the unit circle. Special emphasis is given to the study of the virial coefficients and the specific heat of this gas. In particular, it is shown that if any state can accommodate up to p q-fermions, then the first p virial coefficients of such a gas are the same as that of a gas of free bosons. Explicit expressions for the deviation of higher virial coefficients from the corresponding values for a Bose gas are obtained. Further, as for ordinary fermions, it is shown that the …
Solvable Quantum Mechanical Examples Of Broken Supersymmetry, Asim Gangopadhyaya
Dec 1992
Solvable Quantum Mechanical Examples Of Broken Supersymmetry, Asim Gangopadhyaya
Asim Gangopadhyaya
We construct several analytically solvable examples of broken supersymmetry in non-relativistic quantum mechanics. Our examples are motivated from known shape-invariant potentials obeying unbroken supersymmetry and are obtained from them via suitable mapping procedures.
Possibilities For Finite Grand Unification With N = 2 Supersymmetry, Asim Gangopadhyaya
Dec 1983
Possibilities For Finite Grand Unification With N = 2 Supersymmetry, Asim Gangopadhyaya
Asim Gangopadhyaya
We study the prospects for constructing finite grand unified theories using softly broken N = 2 global supersymmetry. The requirement that the supersymmetry breaking scale be of order 103−104 GeV and that the mixing between the observed light fermions and the mirror fermions present in N = 2 theories be small («mW), make it difficult to construct finite grand unified theories based on a large class of simple groups with a realistic symmetry breaking pattern.
