Schrödinger Operators with Exactly Solvable Potentials

2012 ◽  
pp. 279-410
Author(s):  
D. M. Gitman ◽  
I. V. Tyutin ◽  
B. L. Voronov
Keyword(s):  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Solvable Potentials ◽  
Exactly Solvable Potentials ◽  
Exactly Solvable

The quasi-exactly solvable potentials method applied to the three-body problem

2007 ◽  
Vol 322 (5) ◽  
pp. 1034-1042 ◽  
Author(s):  
F. Chafa ◽  
A. Chouchaoui ◽  
M. Hachemane ◽  
F.Z. Ighezou
Keyword(s):  
Body Problem ◽  
Three Body Problem ◽  
Solvable Potentials ◽  
Exactly Solvable Potentials ◽  
Exactly Solvable ◽  
Three Body

scholarly journals SPECTRUM OF THE RELATIVISTIC PARTICLES IN VARIOUS POTENTIALS

2005 ◽  
Vol 20 (12) ◽  
pp. 911-921 ◽  
Author(s):  
RAMAZAN KOÇ ◽  
MEHMET KOCA
Keyword(s):  
Quantum Mechanics ◽  
Hypergeometric Functions ◽  
Two Dimensions ◽  
Dirac Oscillator ◽  
Confluent Hypergeometric Functions ◽  
Solvable Potentials ◽  
Exactly Solvable Potentials ◽  
Exactly Solvable ◽  
Nonrelativistic Quantum Mechanics ◽  
Relativistic Particles

We extend the notion of Dirac oscillator in two dimensions, to construct a set of potentials. These potentials become exactly and quasi-exactly solvable potentials of nonrelativistic quantum mechanics when they are transformed into a Schrödinger-like equation. For the exactly solvable potentials, eigenvalues are calculated and eigenfunctions are given by confluent hypergeometric functions. It is shown that, our formulation also leads to the study of those potentials in the framework of the supersymmetric quantum mechanics.

scholarly journals QUASI-EXACTLY SOLVABLE MATRIX SCHRÖDINGER OPERATORS

2000 ◽  
Vol 15 (26) ◽  
pp. 1647-1653 ◽  
Author(s):  
YVES BRIHAYE
Keyword(s):  
Polynomial Matrix ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Lamé Equation ◽  
Matrix Potential ◽  
Exactly Solvable ◽  
The Relationship

Two families of quasi-exactly solvable 2×2 matrix Schrödinger operators are constructed. The first one is based on a polynomial matrix potential and depends on three parameters. The second is a one-parameter generalization of the scalar Lamé equation. The relationship between these operators and QES Hamiltonians already considered in the literature is pointed out.

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