Arvind Narayan Vaidya

Algebraic calculation of the Green’s function for the Hartmann potential

Using the so(2,1) Lie algebra and the Baker–Campbell–Hausdorff formulas, the Green’s function for the Hartmann potential is constructed and its bound state energy spectrum is found. Also, this Green’s function is constructed in a coherent state basis and the equivalence of the two descriptions is shown.

Can Galilean mechanics and full Maxwell equations coexist peacefully

Abstract Contrary to what has appeared in literature, we prove that the answer to the question raised in the title is “No, they cannot”.

Algebraic solution of an anisotropic ring-shaped oscillator

Instituto de Fisica Universidade Federal do Rio de Janeiro, Rio de Janeiro 21944, CxP, 68528 RJ

Algebraic solution of an anisotropic nonquadratic potential

Universidade Estadual Paulista, Campus Guaratingueta, DFQ, Av. Dr. Ariberto P. da Cunha 333, 12500 Guaratingueta, SP

A class of double-well like potentials in 1 + 1 dimensions via SUSY QM

The connection between the soliton solutions for potentials in 1 + 1 dimensions and supersymmetry in the context of non-relativistic quantum mechanics is explored. Examining the equivalence between a supersymmetric partner and the stability equation of the model, which is a Schrodinger-like equation for the normal modes, we construct two new supersymmetric partners, which leads us to a new class of isospectral potentials in quantum mechanics and a new class of potential nonlinear models in bidimensional spacetime. We show that such new potentials in 1 + 1 dimensions are double-well like potentials.

Schwinger's method for the electron propagator in a plane wave field revisited

Abstract We reobtain the Green function for a spin 1 2 charged particle in the external field of a (linearly polarized) plane wave using Schwingers method. In our solution, the spin 1 2 case is obtained directly from the spinless case through an algebraic procedure, and the Heisenberg equations involved are integrated in an extremely dimple way.

Algebraic calculation of the S-matrix for the Dirac–Coulomb problem in 2+1 dimensions

We calculate the S-matrix for the Dirac–Coulomb problem in 2+1 dimensions by an algebraic technique.

S-matrix for a spin-1/2 particle in a Coulomb and scalar potential

The S-matrix for a spin-1/2 particle in the presence of a potential which is the sum of the Coulomb potential Vc = −A1/r and a Lorentz scalar potential Vs = −A2/r is calculated.

A SUSY formulation àla Witten for the SUSY isotonic oscillator canonical supercoherent states

We extend Wittens supersymmetry (SUSY) formulation for Hamiltonian systems to a system of annihilation operator eigenvalue equations associated with the SUSY isotonic oscillator, which, as we show, define SUSY canonical supercoherent states containing mixtures of both pure bosonic and pure fermionic counterparts. Specifically, a graded Lie algebra structure analogous to Wittens SUSY quantum mechanical algebra is realized in which only annihilation operators participate, all expressed in terms of the Wigner annihilation operator of a related super-Wigner oscillator system.

Furry’s picture in the path integral framework

SummaryWe obtain the Feynman rules for QED in the presence of an external field in the path integral framework, establishing this way the path integral version of Furry’s picture. We illustrate our method by constructing explicitly the exact path integral expression for the propagator of a relativistic charged particle of spin one-half in the presence of a plane-wave external field.