# The factorization of the hypergeometric equation

@article{Schroedinger1999TheFO, title={The factorization of the hypergeometric equation}, author={Erwin Schroedinger}, journal={arXiv: History and Philosophy of Physics}, year={1999} }

Schroedinger's famous quadruple of factorizations of the hypergeometric equation is archived here

## 35 Citations

### Factorization method for difference equations of hypergeometric type on nonuniform lattices

- Mathematics
- 2001

We study the factorization of the hypergeometric-type difference equation of Nikiforov and Uvarov on nonuniform lattices. An explicit form of the raising and lowering operators is derived and some…

### Remarks on Multi-Dimensional Conformal Mechanics ?

- Physics, Mathematics
- 2009

Recently, Galajinsky, Lechtenfeld and Polovnikov proposed an elegant group- theoretical transformation of the generic conformal-invariant mechanics to the free one. Considering the classical…

### RICCATI EQUATION, FACTORIZATION METHOD AND SHAPE INVARIANCE

- Mathematics
- 2000

The basic concepts of factorizable problems in one-dimensional Quantum Mechanics, as well as the theory of Shape Invariant potentials are reviewed. The relation of this last theory with a…

### Superalgebras for the 3D Harmonic Oscillator and Morse Quantum Potentials

- Physics
- 2004

Abstract In addition to obtaining supersymmetric structure related to the partner Hamiltonians, we get another supersymmetric structure via factorization method for both the 3D harmonic oscillator…

### LAME EQUATION IN THE WEIERSTRASS FORM AND EXACT SOLVABILITY

- Mathematics
- 2016

In this paper, we construct some exactly solvable potentials giving rise to solutions of the Lam\'e equation in the Weierstrass form which can be written in terms of associated Legendre, Hermite, and…

### Coulomb-oscillator duality in spaces of constant curvature

- Mathematics
- 2000

In this paper we construct generalizations to spheres of the well-known Levi-Civita, Kustaanheimo–Steifel, and Hurwitz regularizing transformations in Euclidean spaces of dimensions two, three, and…

### Two new integrable cases of two-dimensional quantum mechanics with a magnetic field

- Physics
- 2016

Two integrable cases of two-dimensional Schrödinger equation with a magnetic field are proposed. Using the polar coordinates and the symmetrical gauge, we will obtain solutions of these equations…

### The Coulomb-oscillator relation on n-dimensional spheres and hyperboloids

- Physics, Mathematics
- 2002

We establish a relation between Coulomb and oscillator systems on n-dimensional spheres and hyperboloids for n≥2. We show that, as in Euclidean space, the quasiradial equation for the…

### Exact solutions of a particle in a box with a delta function potential: The factorization method

- Mathematics, Physics
- 2010

We use the factorization method to find the exact eigenvalues and eigenfunctions for a particle in a box with the delta function potential V(x)=λδ(x−x0). We show that the presence of the potential…

### Mathematical methods of factorization and a feedback approach for biological systems

- Mathematics
- 2005

The first part of the thesis is devoted to factorizations of linear and nonlinear differential equations leading to solutions of the kink type. The second part contains a study of the synchronization…