Journal of Nonlinear Mathematical Physics

Volume 12, Issue Supplement 1, January 2005, Pages 32 - 42

Some Group Theoretical Aspects of Nonlinear Quantal Oscillators

Authors
K ANDRIOPOULOS, P G L LEACH
Corresponding Author
K ANDRIOPOULOS
Available Online 1 January 2005.
DOI
https://doi.org/10.2991/jnmp.2005.12.s1.3How to use a DOI?
Abstract
We investigate the algebraic properties of the time-dependent Schrödinger equations of certain nonlinear oscillators introduced by Calogero and Graffi (Calogero F & Graffi S, On the quantisation of a nonlinear Hamiltonian oscillator Physics Letters A 313 (2003) 356-362; Calogero F, On the quantisation of two other nonlinear harmonic oscillators Physics Letters A 319 (2003) 240-245; Calogero F, On the quantisation of yet another two nonlinear harmonic oscillators Journal of Nonlinear Mathematical Physics 11 (2004) 1-6). Although all of the corresponding classical Hamiltonians are characterised by the Lie algebra sl(2, R), we find that the algebras in the quantal case are not unique and depend upon the choice of parameters made in the quantisation process.
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
12 - 100
Pages
32 - 42
Publication Date
2005/01
ISBN
91-974824-3-9
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.2005.12.s1.3How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - K ANDRIOPOULOS
AU  - P G L LEACH
PY  - 2005
DA  - 2005/01
TI  - Some Group Theoretical Aspects of Nonlinear Quantal Oscillators
JO  - Journal of Nonlinear Mathematical Physics
SP  - 32
EP  - 42
VL  - 12
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2005.12.s1.3
DO  - https://doi.org/10.2991/jnmp.2005.12.s1.3
ID  - ANDRIOPOULOS2005
ER  -