Quantum Hamilton--Jacobi Approach to Two Dimensional Singular Oscillator
Ozlem Yesiltas1, Bengu Demircioglu2
1Gazi University, Faculty of Arts and Sciences, Physics Department, 06500 Teknikokullar, Ankara, Turkey2Ankara University, Faculty of Sciences,Department of Physics, 06100 Tandou gan, Ankara, Turkey
Quantum Hamilton--Jacobi Approach to Two Dimensional Singular Oscillator
Ozlem Yesiltas1;Bengu Demircioglu2
1Gazi University, Faculty of Arts and Sciences, Physics Department, 06500 Teknikokullar, Ankara, Turkey2Ankara University, Faculty of Sciences,Department of Physics, 06100 Tandou gan, Ankara, Turkey
摘要We obtain the solutions of two-dimensional singular oscillator which is known as the quantum Calogero--Sutherland model both in cartesian and parabolic coordinates within the framework of quantum Hamilton Jacobi formalism. Solvability conditions and eigenfunctions are obtained by using the singularity structures of quantum momentum functions under some conditions. New potentials are generated by using the first two states of singular oscillator for parabolic coordinates.
Abstract：We obtain the solutions of two-dimensional singular oscillator which is known as the quantum Calogero--Sutherland model both in cartesian and parabolic coordinates within the framework of quantum Hamilton Jacobi formalism. Solvability conditions and eigenfunctions are obtained by using the singularity structures of quantum momentum functions under some conditions. New potentials are generated by using the first two states of singular oscillator for parabolic coordinates.
[1] Bender C M and Wang Q 2001 J. Phys. A: Math. Gen. 34 9835 Dong S H, Sun G H and Cassou M L 2005 Phys. Lett. A 340 94 [2] Cang Z M and Bang W Z 2005 Chin. Phys. Lett. 22 2994 [3] Kalnins E G, Miller W Jr and Pogosyan G S 2006 J. Math. Phys. 47 033502 [4] Turbiner A V 1988 Comm. Math. Phys. 118 467 [5] Ushveridze A G 1994 Quasi-Exactly Solvable Models in Quantum Mechanics (Washington: Taylor and Francis) [6] Leacock R A and Padgett M J 1983 Phys. Rev. Lett 50 3 Leacock R A and Padgett M J 1983 Phys. Rev. D 282491 [7] Bhalla R S, Kapoor A K and Panigrahi P K 1997 Am. J. Phys. 65 1187 Ranjani S S, Kapoor A K and Panigrahi P K 2005 Int. J. Mod. Phys. A 20 4067 (and the references therein.) [8] Calogero F 1971 J. Math. Phys. 12 419 [9] Infeld L and Hull T E 1951 Rev. Mod. Phys. 23 21 [10] Dong S H 2007 Factorization Method in Quantum Mechanics (Berlin: Springer) [11] Arfken G B 1995 Mathematical Methods for Physicists (London: Academic) [12] \"{Ozlem Ye\c{silta\c{s and Beng\"{u Demircio\~{glu, arXiv:0708.2552. [13] Perelomov A 1986 Generalized Coherent States and Their Applications (Berlin: Springer)
2008, Vol. 25 
