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Articles 1 - 20 of 20
Full-Text Articles in Physics
New Exactly Solvable Hamiltonians - Shape Invariance And Self-Similarity, David Barclay, Ranabir Dutt, Asim Gangopadhyaya, Avinash Khare, A. Pagnamenta, Uday Sukhatne
New Exactly Solvable Hamiltonians - Shape Invariance And Self-Similarity, David Barclay, Ranabir Dutt, Asim Gangopadhyaya, Avinash Khare, A. Pagnamenta, Uday Sukhatne
Asim Gangopadhyaya
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 …
Generation Of A Complete Set Of Additive Shape-Invariant Potentials From An Euler Equation, Jonathan Bougie, Asim Gangopadhyaya, Jeffrey Mallow
Generation Of A Complete Set Of Additive Shape-Invariant Potentials From An Euler Equation, Jonathan Bougie, Asim Gangopadhyaya, Jeffrey Mallow
Asim Gangopadhyaya
In supersymmetric quantum mechanics, shape invariance is a sufficient condition for solvability. We show that all conventional additive shape-invariant superpotentials that are independent of ħ can be generated from two partial differential equations. One of these is equivalent to the one-dimensional Euler equation expressing momentum conservation for inviscid fluid flow, and it is closed by the other. We solve these equations, generate the set of all conventional shape-invariant superpotentials, and show that there are no others in this category. We then develop an algorithm for generating all additive shape-invariant superpotentials including those that depend on ħ explicitly.
Supersymmetry And The Tunneling Problem In An Asymmetric Double Well, Asim Gangopadhyaya, Prasanta Panigrahi, Uday Sukhatne
Supersymmetry And The Tunneling Problem In An Asymmetric Double Well, Asim Gangopadhyaya, Prasanta Panigrahi, Uday Sukhatne
Asim Gangopadhyaya
The techniques of supersymmetric quantum mechanics are applied to the calculation of the energy difference between the ground state and the first excited state of an asymmetric double well. This splitting, originating from the tunneling effect, is computed via a systematic, rapidly converging perturbation expansion. Perturbative calculations to any order can be easily carried out using a logarithmic perturbation theory. Our approach yield substantially better results than alternative widely used semiclassical analyses.
Magnet Traveling Through A Conducting Pipe: A Variation On The Analytical Approach, Benjamin Irvine, Matthew Kemnetz, Asim Gangopadhyaya, Thomas Ruubel
Magnet Traveling Through A Conducting Pipe: A Variation On The Analytical Approach, Benjamin Irvine, Matthew Kemnetz, Asim Gangopadhyaya, Thomas Ruubel
Asim Gangopadhyaya
We present an analytical study of magnetic damping. In particular, we investigate the dynamics of a cylindrical neodymium magnet as it moves through a conducting tube. Owing to the very high degree of uniformity of the magnetization for neodymium magnets, we are able to provide completely analytical results for the electromotive force generated in the pipe and the consequent retarding force. Our analytical expressions are shown to have excellent agreement with experimental observations.
Noncentral Potentials And Spherical Harmonics Using Supersymmetry And Shape Invariance, Ranabir Dutt, Asim Gangopadhyaya, Uday Sukhatne
Noncentral Potentials And Spherical Harmonics Using Supersymmetry And Shape Invariance, Ranabir Dutt, Asim Gangopadhyaya, Uday Sukhatne
Asim Gangopadhyaya
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.
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
Asim Gangopadhyaya
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.
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
Asim Gangopadhyaya
No abstract provided.
Semiclassical Approach To Quantum-Mechanical Problems With Broken Supersymmetry, Ranabir Dutt, Asim Gangopadhyaya, Avinash Khare, A. Pagnamenta, Uday Sukhatne
Semiclassical Approach To Quantum-Mechanical Problems With Broken Supersymmetry, Ranabir Dutt, Asim Gangopadhyaya, Avinash Khare, A. Pagnamenta, Uday Sukhatne
Asim Gangopadhyaya
The semiclassical WKB approximation method is reexamined in the context of nonrelativistic quantum-mechanical bound-state problems with broken supersymmetry (SUSY). This gives rise to an alternative quantization condition (denoted by BSWKB) which is different from the standard WKB formula and also different from the previously studied supersymmetric (SWKB) formula for unbroken SUSY. It is shown that to leading order in ħ, the BSWKB condition yields exact energy eigenvalues for shape-invariant potentials with broken SUSY (harmonic oscillator, Pöschl-Teller I and II) which are known to be analytically solvable. Further, we show explicitly that the higher-order corrections to these energy eigenvalues, up to …
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
Asim Gangopadhyaya
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.
Comment On ‘‘The Hidden Symmetry For A Quantum System With An Infinitely Deep Square-Well Potential By Shi-Hai Dong And Zhong-Qi Ma [Am. J. Phys. 70 (5) 520-521 (2002)], Asim Gangopadhyaya, Jeffrey Mallow
Comment On ‘‘The Hidden Symmetry For A Quantum System With An Infinitely Deep Square-Well Potential By Shi-Hai Dong And Zhong-Qi Ma [Am. J. Phys. 70 (5) 520-521 (2002)], Asim Gangopadhyaya, Jeffrey Mallow
Asim Gangopadhyaya
No abstract provided.
Gravitational Slingshot , John Dykla, Robert Cacioppo, Asim Gangopadhyaya
Gravitational Slingshot , John Dykla, Robert Cacioppo, Asim Gangopadhyaya
Asim Gangopadhyaya
The slingshot effect is an intriguing phenomenon that has been used effectively by NASA to send spacecraft to outer edges of the solar system. This phenomenon can be satisfactorily explained by Newtonian physics. However, if it is presented as a problem involving four-momentum conservation, the methods of relativistic kinematics easily lead to the conditions necessary for an accelerating as well as a retarding scenario. This problem provides an example that showcases the frequent utility of relativistic methods to analyze problems of Newtonian mechanics.
New Solvable Singular Potentials , R. Dutt, Asim Gangopadhyaya, C. Rasinariu, Uday Sukhatne
New Solvable Singular Potentials , R. Dutt, Asim Gangopadhyaya, C. Rasinariu, Uday Sukhatne
Asim Gangopadhyaya
We obtain three new solvable, real, shape invariant potentials starting from the harmonic oscillator, Pöschl-Teller I and Pöschl-Teller II potentials on the half-axis and extending their domain to the full line, while taking special care to regularize the inverse square singularity at the origin. The regularization procedure gives rise to a delta-function behavior at the origin. Our new systems possess underlying non-linear potential algebras, which can also be used to determine their spectra analytically.
Inter-Relations Of Solvable Potentials, Asim Gangopadhyaya, Prasanta Panigrahi, Uday Sukhatne
Inter-Relations Of Solvable Potentials, Asim Gangopadhyaya, Prasanta Panigrahi, Uday Sukhatne
Asim Gangopadhyaya
Solvable Natanzon potentials in nonrelativistic quantum mechanics are known to group into two disjoint classes depending on whether the Schrödinger equation can be reduced to a hypergeometric or a confluent hypergeometric equation. All the potentials within each class are connected via point canonical transformations. We establish a connection between the two classes with appropriate limiting procedures and redefinition of parameters, thereby inter-relating all known solvable potentials.
Unintended Consequences Of Imprecise Notation – An Example From Mechanics, Asim Gangopadhyaya, Gordon Ramsey
Unintended Consequences Of Imprecise Notation – An Example From Mechanics, Asim Gangopadhyaya, Gordon Ramsey
Asim Gangopadhyaya
We present a conundrum that results from the imprecise use of notation for partial derivatives. Taking an example from mechanics, we show that lack of proper care in re presenting partial derivatives in Lagrangian and Hamiltonian formulations paradoxically leads to two different values for the time derivative of the canonical momentum. This problem also exists in other areas of physics,such as thermodynamics.
Coordinate Realizations Of Deformed Lie Algebras With Three Generator, Ranabir Dutt, Asim Gangopadhyaya, C. Rasinariu, Uday Sukhatne
Coordinate Realizations Of Deformed Lie Algebras With Three Generator, Ranabir Dutt, Asim Gangopadhyaya, C. Rasinariu, Uday Sukhatne
Asim Gangopadhyaya
Differential realizations in coordinate space for deformed Lie algebras with three generators are obtained using bosonic creation and annihilation operators satisfying Heisenberg commutation relations. The unified treatment presented here contains as special cases all previously given coordinate realizations of so(2,1), so(3), and their deformations. Applications to physical problems involving eigenvalue determination in nonrelativistic quantum mechanics are discussed.
Translational Shape Invariance And The Inherent Potential Algebra, Asim Gangopadhyaya, Jeffrey Mallow, Uday Sukhatne
Translational Shape Invariance And The Inherent Potential Algebra, Asim Gangopadhyaya, Jeffrey Mallow, Uday Sukhatne
Asim Gangopadhyaya
For all quantum-mechanical potentials that are known to be exactly solvable, there are two different, and seemingly independent methods of solution. The first approach is the potential algebra of symmetry groups; the second is supersymmetric quantum mechanics, applied to shape-invariant potentials, which comprise the set of known exactly solvable potentials. Using the underlying algebraic structures of Natanzon potentials, of which the translational shape-invariant potentials are a special subset, we demonstrate the equivalence of the two methods of solution. In addition, we show that, while the algebra for the general Natanzon potential is so(2,2), the subgroup so(2,1) suffices for the shape …
Anyonic Superconductivity In A Modified Large-U Hubbard Model, Asim Gangopadhyaya, Prasanta Panigrahi
Anyonic Superconductivity In A Modified Large-U Hubbard Model, Asim Gangopadhyaya, Prasanta Panigrahi
Asim Gangopadhyaya
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.
Superspace Ward Identities In Supersymmetric Gauge Theories, Asim Gangopadhyaya, Darwin Chang
Superspace Ward Identities In Supersymmetric Gauge Theories, Asim Gangopadhyaya, Darwin Chang
Asim Gangopadhyaya
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.
The Electric Field At The Chargeless Interface Between Two Regions Of Space, Asim Gangopadhyaya, Robert Mcnees
The Electric Field At The Chargeless Interface Between Two Regions Of Space, Asim Gangopadhyaya, Robert Mcnees
Asim Gangopadhyaya
A common method for solving Poisson's equation in electrostatics is to patch together two or more solutions of Laplace's equation using boundary conditions on the potential and its gradient. Other methods may generate solutions without the need to check these conditions explicitly, and reconciling these solutions with the appropriate boundary conditions can be surprisingly subtle. As a result, a student may arrive at paradoxical conclusions—even in the case of elementary problems—that seem to be at odds with basic physical intuition. We illustrate this issue by showing how the potential of a uniformly charged ring appears to violate continuity of the …
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
Asim Gangopadhyaya
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.