Related papers: Mapping of shape invariant potentials by the point…
We construct canonical transformations to obtain a complete and most economical realization of the physical Hilbert space ${\cal H}^p$ of pure $SU(2)_{2+1}$ lattice gauge theory in terms of Wigner coupled Hilbert spaces of hydrogen atoms.…
In this paper we discuss the quantum potential approach of Bohm in the context of quantum cosmological model. This approach makes it possible to convert the wavefunction of the universe to a set of equations describing the time evolution of…
Using hyperbolic form convolution with doubly isometry-invariant kernels, the explicit expression of the inverse of the de Rham laplacian acting on m-forms in the Poincar\'{e} space is found. Also, by means of some estimates for hyperbolic…
Using mainly two techniques, a point transformation and a time dependent supersymmetry, we construct in sequence several quantum infinite potential wells with a moving barrier. We depart from the well known system of a one-dimensional…
Bialkowski, Erdmann and Skowronski classified those indecomposable self-injective algebras for which the Nakayama shift of every (non-projective) simple module is isomorphic to its third syzygy. It turned out that these are precisely the…
In this note we prove some structural properties of all the A1-homotopy invariants of corner skew Laurent polynomial algebras. As an application, we compute de mod-l algebraic K-theory of Leavitt path algebras using solely the…
We consider the quantized $\mathrm{SL}_2$-character variety of a once-punctured torus. We show that this quantized algebra has three $\mathbb{Z}_2$-invariant subalgebras that are isomorphic to quantized $K$-theoretic Coulomb branches in the…
We provide a model for an open invariant neighborhood of any orbit in a symplectic manifold endowed with a canonical proper symmetry. Our results generalize the constructions of Marle and Guillemin and Sternberg for canonical symmetries…
Point canonical transformation (PCT) has been used to find out new exactly solvable potentials in the position-dependent mass (PDM) framework. We solve $1$-D Schr\"{o}dinger equation in the PDM framework by considering two different fairly…
Using the method of shape invariant potentials, a number of exact solutions of one dimensional effective mass Schrodinger equation are obtained. The solutions with equi-spaced spectrum are discussed in detail.
We analyze the low energy behavior of N=1 supersymmetric gauge theories with SU(N_c) x SU(N_c) gauge group and a Landau-Ginzburg type superpotential. These theories contain fundamentals transforming under one of the gauge groups as well as…
Shape Invariant potentials in the sense of [Gendenshte\"{\i}n L.\'E., JETP Lett. 38, (1983) 356] which depend on more than two parameters are not know to date. In [Cooper F., Ginocchio J.N. and Khare A., Phys. Rev. {\bf 36 D}, (1987) 2458]…
By using the point canonical transformation approach in a manner distinct from previous ones, we generate some new exactly solvable or quasi-exactly solvable potentials for the one-dimensional Schr\"odinger equation with a…
Bound-state solutions of the singular harmonic oscillator and singular Coulomb potentials in arbitrary dimensions are generated in a simple way from the solutions of the one-dimensional generalized Morse potential. The nonsingular harmonic…
Using the shape invariance property we obtain exact solutions of the (1+1)dimensional Klein-Gordon equation for certain types of scalar and vector potentials. We also discuss the possibility of obtaining real energy spectrum with…
Some results about non-bijective quadratic transformations generalizing the Kustaanheimo-Stiefel and the Levi-Civita transformations are reviewed in \S 1. The three remaining sections are devoted to new results: \S 2 deals with the Lie…
An algebraic treatment of shape-invariant potentials in supersymmetric quantum mechanics is discussed. By introducing an operator which reparametrizes wave functions, the shape-invariance condition can be related to a oscillator-like…
Spin-one matter fields are relevant both for the description of hadronic states and as potential extensions of the Standard Model. In this work we present a formalism for the description of massive spin-one fields transforming in the…
By using a point canonical transformation starting from the constant-mass Schr\"odinger equation for the Morse potential, it is shown that a semi-infinite quantum well model with a non-rectangular profile associated with a…
The time-dependent, geometric method for high-energy limits and inverse scattering is applied to nonrelativistic quantum particles in external electromagnetic fields. Both the Schr"odinger- and the Pauli equations in R^2 and R^3 are…