相关论文: New results concerning the $so(2,1)$ treatment for…
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.
The $so(2,1)$ Euclidean Connection formalism is used to calculate the $S$ matrix for the Hypergeometric Natanzon Potentials ($HNP$).
We study in detail the bound state spectrum of the generalized Morse potential~(GMP), which was proposed by Deng and Fan as a potential function for diatomic molecules. By connecting the corresponding Schr\"odinger equation with the Laplace…
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…
A new manner for deriving the exact potentials is presented. By making use of conformal mappings, the general expression of the effective potentials deduced under su(1,1) algebra can be brought back to the general Natanzon hypergeometric…
SO(2,1) is the symmetry algebra for a class of three-parameter problems that includes the oscillator, Coulomb and Morse potentials as well as other problems at zero energy. All of the potentials in this class can be mapped into the…
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.
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…
The so$(2,1)$ Lie algebra is applied to three classes of two- and three-dimensional Smorodinsky-Winternitz super-integrable potentials for which the path integral discussion has been recently presented in the literature. We have constructed…
The peculiarity of the Eckart potential problem on ${\bf H}^2_+$ (the upper sheet of the two-sheeted two-dimensional hyperboloid), to preserve the $(2l+1)$-fold degeneracy of the states typical for the geodesic motion there, is usually…
Recently, we introduced a new class of symmetry algebras, called satellite algebras, which connect with one another wavefunctions belonging to different potentials of a given family, and corresponding to different energy eigenvalues. Here…
We study the quantum mechanics of a system with inverse square potential in noncommutative space. Both the coordinates and momentums are considered to be noncommutative, which breaks the original so(2,1) symmetry. The energy levels and…
Using the method of $su(1,1)$ spectrum generating algebra, we analyze one dimensional Schroedinger equation with potential in the form ${C\over{x^2} + {D\over{x}}$ to obtain a class of potentials giving similar eigenvalues. By a group…
Bound and scattering states of a non-central extension of the three-dimensional Kepler-Coulomb Hamiltonian are worked out analytically within the framework of the potential groups of the problem, SO(7) for bound states and SO(6,1) for…
A novel spin-extended so($d+1$,1) algebra is introduced and shown to provide an interesting framework for discussing the properties of a $d$-dimensional matrix Hamiltonian with spin 1/2 and so($d+1$) symmetry. With some $d+2$ additional…
Quasi-exactly solvable rational potentials with known zero-energy solutions of the Schro\" odinger equation are constructed by starting from exactly solvable potentials for which the Schr\" odinger equation admits an so(2,1) potential…
We present a new six-parameter family of potentials whose solutions are expressed in terms of the hypergeometric functions 3F2, 2F2 and 1F2. Both the scattering data and the bound states of these potentials are explicitly computed and the…
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 in a systematic and clear way how factorization methods can be used to construct the generators for hidden and dynamical symmetries. This is shown by studying the 2D problems of hydrogen atom, the isotropic harmonic oscillator and…
Various methods to obtain the analytic continuation near $z=1$ of the hypergeometric series $_{p+1}F_p(z)$ are reviewed together with some of the results. One approach is to establish a recurrence relation with respect to $p$ and then,…