# SO(2, 1), Supersymmetry and D-Dimensional Radial Schrödinger Equation

About: This article is published in Progress of Theoretical Physics.The article was published on 1995-08-01 and is currently open access. It has received 3 citations till now. The article focuses on the topics: Supersymmetric quantum mechanics & Quantum statistical mechanics.

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TL;DR: In this article, the bound-state solutions and the su(1,1) description of the d-dimensional radial harmonic oscillator, the Morse and Coulomb Schrodinger equations are reviewed in a unified way using the point canonical transformation method.

Abstract: The bound-state solutions and the su(1,1) description of the d-dimensional radial harmonic oscillator, the Morse, and the D-dimensional radial Coulomb Schrodinger equations are reviewed in a unified way using the point canonical transformation method. It is established that the spectrum generating su(1,1) algebra for the first problem is converted into a potential algebra for the remaining two. This analysis is then extended to Schrodinger equations containing some position-dependent mass. The deformed su(1,1) construction recently achieved for a d-dimensional radial harmonic oscillator is easily extended to the Morse and Coulomb potentials. In the last two cases, the equivalence between the resulting deformed su(1,1) potential algebra approach and a previous deformed shape invariance one generalizes to a position-dependent mass background a well-known relationship in the context of constant mass.

20 citations

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TL;DR: In this paper, the bound-state solutions and the su(1,1) description of the $d$-dimensional radial harmonic oscillator, the Morse and the radial Coulomb Schrodinger equations are reviewed in a unified way using the point canonical transformation method.

Abstract: The bound-state solutions and the su(1,1) description of the $d$-dimensional radial harmonic oscillator, the Morse and the $D$-dimensional radial Coulomb Schrodinger equations are reviewed in a unified way using the point canonical transformation method. It is established that the spectrum generating su(1,1) algebra for the first problem is converted into a potential algebra for the remaining two. This analysis is then extended to Schrodinger equations containing some position-dependent mass. The deformed su(1,1) construction recently achieved for a $d$-dimensional radial harmonic oscillator is easily extended to the Morse and Coulomb potentials. In the last two cases, the equivalence between the resulting deformed su(1,1) potential algebra approach and a previous deformed shape invariance one generalizes to a position-dependent mass background a well-known relationship in the context of constant mass.

12 citations

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TL;DR: In this paper, the symmetry transformations preserving the radial form of the Schrodinger equation lead to matching conditions which are essentially the same as the classical ones, and power-law potentials are treated as illustrative examples.

Abstract: Proofs are given that the symmetry transformations preserving the radial form of the Schrodinger equation lead to matching conditions which are essentially the same as the classical ones. Power-law potentials are treated as illustrative examples. In particular, the -dimensional q-deformed Coulomb system is converted into a q-deformed harmonic oscillator acting again in space dimensions. We also found that q-deformed 1/N energy formulae are covariant under such transformations to first 1/N-order.

4 citations

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TL;DR: The eigenvalues and eigenfunctions of the nonrelativistic hydrogen atom were obtained using supersymmetric quantum mechanics arguments and basic properties of the Schrodinger equation.

Abstract: The eigenvalues and eigenfunctions of the nonrelativistic hydrogen atom are obtained using supersymmetric quantum mechanics arguments and basic properties of the Schrodinger equation.

12 citations