Related papers: A Group-Theoretical Method for Natanzon Potentials…
Using the underlying algebraic structures of Natanzon potentials, we discuss conditions that generate shape invariant potentials. In fact, these conditions give all the known shape invariant potentials corresponding to a translational…
As a result of the so(2,1) of the hypergeometric Natanzon potential a set of potentials related to the given one is determined. The set arises as a result of the action of the so(2,1) generators.
An algebraic method of constructing potentials for which the Schroedinger equation with position dependent mass can be solved exactly is presented. A general form of the generators of su(1,1) algebra has been employed with a unified…
A new class of quasi exactly solvable potentials with a variable mass in the Schroedinger equation is presented. We have derived a general expression for the potentials also including Natanzon confluent potentials. The general solution of…
The differential realization of the potential group SO(2,2) is used. The spectrum-generating algebra for a kind of exactly solvable potentials endowed with position-dependent mass is constructed.
The $so(2,1)$ analysis for the bound state sector of the hypergeometric Natanzon potentials (HNP) is extended to the scattering sector by considering the continuous series of the $so(2,1)$ algebra. As a result a complete algebraic treatment…
The $so(2,1)$ Euclidean Connection formalism is used to calculate the $S$ matrix for the Hypergeometric Natanzon Potentials ($HNP$).
We apply effective field theory (EFT) methods to compute the renormalization group improved effective potential for theories with a large mass hierarchy. Our method allows one to compute the effective potential in a systematic expansion in…
Four new exactly solvable, real and shape-invariant potentials associated with a position-dependent effective mass are generated within the concept of shape-invariant potentials using a specific ansatz for superpotential. The accompanying…
There is a general mechanism by which certain matter fields coupled to gravity can generate a nontrivial effective potential for the conformal factor of the metric. It is based on a nonstandard regularization method, with the cutoff being…
An algebraic method of constructing the confluent Natanzon potentials endowed with position-dependent mass is presented. This is possible by identifying the scaling resolvent operator (Green's function) to nonrelativistic position-dependent…
We discuss the ways of constructing the exact superpotential for N=1 supersymmetric theories and propose a new approach. As a consequence, a new structure of the superpotential is found.
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…
We show that the evolution equation of the effective potential in the auxiliary mass method corresponds to a leading approximation of a certain series. This series is derived from an evolution equation of an effective action using a…
It is well known that effective potentials can be gauge-dependent while their values at extrema should be gauge-invariant. Unfortunately, establishing this invariance in perturbation theory is not straightforward, since contributions from…
A one-dimensional Schr\"odinger equation with position-dependent effective mass in the kinetic energy operator is studied in the framework of an $so(2,1)$ algebra. New mass-deformed versions of Scarf II, Morse and generalized…
An exact superpotential is derived for the N=1 theories which arise as massive deformations of N=4 supersymmetric Yang-Mills (SYM) theory. The superpotential of the SU(N) theory formulated on R^{3}\times S^{1} is shown to coincide with the…
Solvable Natanzon potentials in nonrelativistic quantum mechanics are known to group into two disjoint classes depending on whether the Schr\"odinger equation can be reduced to a hypergeometric or a confluent hypergeometric equation. All…
Previously proposed procedure for improving the effective potential by using renormalization group equation (RGE) is generalized so as to be applicable to any system containing several different mass scales. If one knows L-loop effective…
The renormalization group method is employed to study the effective potential in curved spacetime with torsion. The renormalization-group improved effective potential corresponding to a massless gauge theory in such a spacetime is found and…