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Articles 1 - 17 of 17
Full-Text Articles in Quantum Physics
Supersymmetric Quantum Mechanics And Solvable Models, Asim Gangopadhyaya, Jonathan Bougie, Jeffrey Mallow, C. Rasinariu
Supersymmetric Quantum Mechanics And Solvable Models, Asim Gangopadhyaya, Jonathan Bougie, Jeffrey Mallow, C. Rasinariu
Physics: Faculty Publications and Other Works
We review solvable models within the framework of supersymmetric quantum mechanics (SUSYQM). In SUSYQM, the shape invariance condition insures solvability of quantum mechanical problems. We review shape invariance and its connection to a consequent potential algebra. The additive shape invariance condition is specified by a difference-differential equation; we show that this equation is equivalent to an infinite set of partial differential equations. Solving these equations, we show that the known list of h-independent superpotentials is complete. We then describe how these equations could be extended to include superpotentials that do depend on h.
Shape Invariance And The Exactness Of Quantum Hamilton-Jacobi Formalism, Charles Cherqui, Yevgeny Binder, Asim Gangopadhyaya
Shape Invariance And The Exactness Of Quantum Hamilton-Jacobi Formalism, Charles Cherqui, Yevgeny Binder, Asim Gangopadhyaya
Physics: Faculty Publications and Other Works
Quantum Hamilton-Jacobi Theory and supersymmetric quantum mechanics (SUSYQM) are two parallel methods to determine the spectra of a quantum mechanical systems without solving the Schr ̈odinger equation. It was recently shown that the shape invariance, which is an integrability condition in SUSYQM formalism, can be utilized to develop an iterative algorithm to determine the quantum momentum functions. In this paper, we show that shape invariance also suffices to determine the eigenvalues in Quantum Hamilton-Jacobi Theory.
Shape Invariance In Supersymmetric Quantum Mechanics And Its Application To Selected Special Functions Of Modern Physics, Chad Husko, Brenton Knuffman, Asim Gangopadhyaya, Jeffrey Mallow
Shape Invariance In Supersymmetric Quantum Mechanics And Its Application To Selected Special Functions Of Modern Physics, Chad Husko, Brenton Knuffman, Asim Gangopadhyaya, Jeffrey Mallow
Physics: Faculty Publications and Other Works
We applied the methods of supersymmetric quantum mechanics to differential equations that generate well-known special functions of modern physics. This application provides new insight into these functions and generates recursion relations among them. Some of these recursion relations are apparently new (or forgotten), as they are not available in commonly used texts and handbooks. This method can be easily extended to explore other special functions of modern physics.
Exactly Solvable Systems And The Quantum Hamilton Jacobi Formalism, C. Rasinariu, John J. Dykla, Asim Gangopadhyaya, Jeffrey Mallow
Exactly Solvable Systems And The Quantum Hamilton Jacobi Formalism, C. Rasinariu, John J. Dykla, Asim Gangopadhyaya, Jeffrey Mallow
Physics: Faculty Publications and Other Works
We connect Quantum Hamilton-Jacobi Theory with supersymmetric quantum mechanics (SUSYQM). We show that the shape invariance, which is an integrability condition of SUSYQM, translates into fractional linear relations among the quantum momentum functions.
Exact Solutions Of The Schroedinger Equation: Connection Between Supersymmetric Quantum Mechanics And Spectrum Generating Algebras, Asim Gangopadhyaya, Jeffrey Mallow, C. Rasinariu, Uday P. Sukhatne
Exact Solutions Of The Schroedinger Equation: Connection Between Supersymmetric Quantum Mechanics And Spectrum Generating Algebras, Asim Gangopadhyaya, Jeffrey Mallow, C. Rasinariu, Uday P. Sukhatne
Physics: Faculty Publications and Other Works
Using supersymmetric quantum mechanics, one can obtain analytic expressions for the eigenvalues and eigenfunctions for all nonrelativistic shape invariant Hamiltonians. These Hamiltonians also possess spectrum generating algebras and are hence solvable by an independent, group theoretical method. In this paper, we demonstrate the equivalence of the two methods of solution, and review related progress in this field.
Broken Supersymmetric Shape Invariant Systems And Their Potential Algebras, Asim Gangopadhyaya, Jeffrey Mallow, Uday P. Sukhatne
Broken Supersymmetric Shape Invariant Systems And Their Potential Algebras, Asim Gangopadhyaya, Jeffrey Mallow, Uday P. Sukhatne
Physics: Faculty Publications and Other Works
Although eigenspectra of one dimensional shape invariant potentials with unbroken supersymmetry are easily obtained, this procedure is not applicable when the parameters in these potentials correspond to broken supersymmetry, since there is no zero energy eigenstate. We describe a novel two-step shape invariance approach as well as a group theoretic potential algebra approach for solving such broken supersymmetry problems.
Comment On "Ideal Capacitor Circuits And Energy Conservation" By K. Mita And M. Boufaida [Am. J. Phys. 67 (8), 737-739 (1999)], Asim Gangopadhyaya, Jeffrey Mallow
Comment On "Ideal Capacitor Circuits And Energy Conservation" By K. Mita And M. Boufaida [Am. J. Phys. 67 (8), 737-739 (1999)], Asim Gangopadhyaya, Jeffrey Mallow
Physics: Faculty Publications and Other Works
No abstract provided.
Algebraic Shape Invariant Models, S Chaturvedi, Ranabir Dutt, Asim Gangopadhyaya, Prasanta K. Panigrahi, C. Rasinariu, Uday P. Sukhatme
Algebraic Shape Invariant Models, S Chaturvedi, Ranabir Dutt, Asim Gangopadhyaya, Prasanta K. Panigrahi, C. Rasinariu, Uday P. Sukhatme
Physics: Faculty Publications and Other Works
Motivated by the shape invariance condition in supersymmetric quantum mechanics, we develop an algebraic framework for shape invariant Hamiltonians with a general change of parameters. This approach involves nonlinear generalizations of Lie algebras. Our work extends previous results showing the equivalence of shape invariant potentials involving translational change of parameters with standard SO (2,1) potential algebra for Natanzon type potentials.
Shape Invariance And Its Connection To Potential Algebra, Asim Gangopadhyaya, Jeffrey Mallow, Uday P. Sukhatme
Shape Invariance And Its Connection To Potential Algebra, Asim Gangopadhyaya, Jeffrey Mallow, Uday P. Sukhatme
Physics: Faculty Publications and Other Works
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.
Potentials With Two Shifted Sets Of Equally Spaced Eigenvalues And Their Calogero Spectrum, Asim Gangopadhyaya, Uday P. Sukhatme
Potentials With Two Shifted Sets Of Equally Spaced Eigenvalues And Their Calogero Spectrum, Asim Gangopadhyaya, Uday P. Sukhatme
Physics: Faculty Publications and Other Works
Motivated by the concept of shape invariance in supersymmetric quantum mechanics, we obtain potentials whose spectrum consists of two shifted sets of equally spaced energy levels. These potentials are similar to the Calogero-Sutherland model except the singular term αx−2 always falls in the transition region -1/4 < a < 3/4 and there is a δ-function singularity at x=0.
Noncentral Potentials And Spherical Harmonics Using Supersymmetry And Shape Invariance, Ranabir Dutt, Asim Gangopadhyaya, Uday P. Sukhatne
Noncentral Potentials And Spherical Harmonics Using Supersymmetry And Shape Invariance, Ranabir Dutt, Asim Gangopadhyaya, Uday P. Sukhatne
Physics: Faculty Publications and Other Works
It is shown that the operator methods of supersymmetric quantum mechanics and the concept of shape invariance can profitably be used to derive properties of spherical harmonics in a simple way. The same operator techniques can also be applied to several problems with noncentral vector and scalar potentials. As examples, we analyze the bound state spectra of an electron in a Coulomb plus an Aharonov – Bohm field and/or in the magnetic field of a Dirac monopole.
New Exactly Solvable Hamiltonians - Shape Invariance And Self-Similarity, David T. Barclay, Ranabir Dutt, Asim Gangopadhyaya, Avinash Khare, A. Pagnamenta, Uday P. Sukhatne
New Exactly Solvable Hamiltonians - Shape Invariance And Self-Similarity, David T. Barclay, Ranabir Dutt, Asim Gangopadhyaya, Avinash Khare, A. Pagnamenta, Uday P. Sukhatne
Physics: Faculty Publications and Other Works
We discuss in some detail the self-similar potentials of Shabat and Spiridonov which are reflectionless and have an infinite number of bound states. We demonstrate that these self-similar potentials are in fact shape invariant potentials within the formalism of supersymmetric quantum mechanics. In particular, using a scaling ansatz for the change of parameters, we obtain a large class of new, reflectionless, shape invariant potentials of which the Shabat-Spiridonov ones are a special case. These new potentials can be viewed as q-deformations of the single soliton solution corresponding to the Rosen-Morse potential. Explicit expressions for the energy eigenvalues, eigenfunctions and transmission …
Anyonic Superconductivity In A Modified Large-U Hubbard Model, Asim Gangopadhyaya, Prasanta K. Panigrahi
Anyonic Superconductivity In A Modified Large-U Hubbard Model, Asim Gangopadhyaya, Prasanta K. Panigrahi
Physics: Faculty Publications and Other Works
A modified large-U Hubbard model at half filling is analyzed by a mean-field approach. Preserving a local U(1) symmetry of the action, the fluctuations about half filling are studied in the spirit of the commensurate-flux-phase condition. The fluctuations then contribute a Chern-Simons term to the tree-level Lagrangian with a coefficient appropriate to that of a half fermion. With the Coulomb repulsion term, we study the low-energy excitations of the model and show the existence of superconductivity in the presence of a four-Fermi interaction term.
Heterotic Conformal Field Theory And Gepner’S Construction, Darwin Chang, Asim Gangopadhyaya, Alok Kumar, Jin Wang
Heterotic Conformal Field Theory And Gepner’S Construction, Darwin Chang, Asim Gangopadhyaya, Alok Kumar, Jin Wang
Physics: Faculty Publications and Other Works
We discuss some general properties of heterotic conformal field theory in which conformal anomalies c are different for the left-moving and right-moving sectors. It is precisely this type of theory that can be applied immediately to the construction of heterotic string theory. We discuss a general way of constructing such a theory using free fermions. The construction is then applied to generalize Gepner's construction of superstring solutions using the tensor products of N=2 superconformal field theories.
Renormalization Group Equations In Broken Supersymmetric Theories Using Superspace Methods, Asim Gangopadhyaya, Darwin Chang
Renormalization Group Equations In Broken Supersymmetric Theories Using Superspace Methods, Asim Gangopadhyaya, Darwin Chang
Physics: Faculty Publications and Other Works
We apply the superfield method with the spurion technique to derive the renormalization-group equations in broken supersymmetric theories. We point out some possible ambiguities in this procedure and show that it is in general necessary to express the supersymmetry-breaking terms in explicit D-type form. We also found that it is possible to construct broken supersymmetric theories where some of the symmetry-breaking parameters do not receive any infinite renormalization.
Kl−Ks Mass Difference And Supersymmetric Left-Right-Symmetric Theories, Asim Gangopadhyaya
Kl−Ks Mass Difference And Supersymmetric Left-Right-Symmetric Theories, Asim Gangopadhyaya
Physics: Faculty Publications and Other Works
The supersymmetric contributions to the KL−KS mass difference makes the previously obtained bounds on the right-handed scale (MR>1.6 TeV) much weaker. This raises the interesting possibility that the left-right model could be tested as an alternative to SUL(2)⊗U(1) at low energies. Also we find that to demand that the supersymmetric contribution to the KL−KS mass difference be less than 3.5×10−15 GeV requires that scalar-quark masses be more than 400 GeV.
Superspace Ward Identities In Supersymmetric Gauge Theories, Asim Gangopadhyaya, Darwin Chang
Superspace Ward Identities In Supersymmetric Gauge Theories, Asim Gangopadhyaya, Darwin Chang
Physics: Faculty Publications and Other Works
In superspace formulation of supersymmetric gauge theories, gauge invariance requires an infinite set of identities between the infinite set of renormalization constants. Using Ward identities in superspace, the same is derived. These identities at one loop level are also demonstrated.