### Journals Information

**
Universal Journal of Physics and Application Vol. 7(1), pp. 10 - 13 DOI: 10.13189/ujpa.2013.010102 Reprint (PDF) (178Kb) **

## An Exactly Solvable Three Dimensional Nonlinear Quantum Oscillator and sl(2) Algebra

**J. Sadeghi ^{*}, M. Rostami**

Department of Physics, Islamic Azad University-Ayatollah Amoli Branch, P.O.Box 678, Amol, Iran

**ABSTRACT**

In this paper, first we introduce the three dimensional non-linear oscillator with a position dependent mass. In that case we start by the stationary Schrodinger equation which is generated by the three dimensional Hamiltonian. The wave function depend on three spatial variables and the usual process of variable in spherical coordinates and the wave functions will be of radial and angular solutions. We can easily solve the angular part of equation but redial part of equation will be complicated. In that case, we take advantage from sl(2) algebra and write the corresponding equation in terms of P_{+}(r), P_{-}(r) and P_{0}(r) which are generators of generalized sl(2) algebra. The information of this algebra help us to obtain the energy spectrum and wave function from radial part of equation.

**KEYWORDS**

Non-Linear Oscillator Potential; sl(2) Algebra; First Order Operators; Energy Spectrum

**Cite This Paper in IEEE or APA Citation Styles**

(a). IEEE Format:

[1] J. Sadeghi , M. Rostami , "An Exactly Solvable Three Dimensional Nonlinear Quantum Oscillator and sl(2) Algebra," Universal Journal of Physics and Application, Vol. 7, No. 1, pp. 10 - 13, 2013. DOI: 10.13189/ujpa.2013.010102.

(b). APA Format:

J. Sadeghi , M. Rostami (2013). An Exactly Solvable Three Dimensional Nonlinear Quantum Oscillator and sl(2) Algebra. Universal Journal of Physics and Application, 7(1), 10 - 13. DOI: 10.13189/ujpa.2013.010102.