Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1138.81380
Cariñena, J.F.; Perelomov, A.M.; Rañada, M.F.; Santander, M.
A quantum exactly solvable nonlinear oscillator related to the isotonic oscillator. (English)
[J] J. Phys. A, Math. Theor. 41, No. 8, Article ID 085301, 10 p. (2008). ISSN 1751-8113; ISSN 1751-8121/e

Summary: A nonpolynomial one-dimensional quantum potential representing an oscillator, which can be considered as placed in the middle between the harmonic oscillator and the isotonic oscillator (harmonic oscillator with a centripetal barrier), is studied. First the general case, that depends on a parameter $a$, is considered and then a particular case is studied with great detail. It is proven that it is Schrödinger solvable and then the wavefunctions $\Psi n$ and the energies $E_{n}$ of the bound states are explicitly obtained. Finally, it is proven that the solutions determine a family of orthogonal polynomials ${\cal P}_n(x) $ related to the Hermite polynomials and such that: (i) every ${\cal P}_n $ is a linear combination of three Hermite polynomials and (ii) they are orthogonal with respect to a new measure obtained by modifying the classic Hermite measure.

MSC 2000:: *81Q05 Closed and approximate solutions to quantum-mechanical equations
81U15 Exactly and quasi-solvable systems
33C45 Orthogonal polynomials and functions of hypergeometric type

Cited in: Zbl 1200.81084 Zbl 1177.81034

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]