Charged particles in external fields as physical examples of quasi-exactly-solvable models: A unified treatment

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Title:	Charged particles in external fields as physical examples of quasi-exactly-solvable models: A unified treatment
Authors:	Chiang, Chun-ming;Ho, Choon-lin
Contributors:	淡江大學物理學系
Keywords:	High Energy Physics - Theory (hep-th);Condensed Matter (cond-mat);Mathematical Physics (math-ph);Spectral Theory (math.SP);Exactly Solvable and Integrable Systems (nlin.SI);Quantum Physics (quant-ph)
Date:	2001-05
Issue Date:	2013-07-09 15:10:42 (UTC+8)
Publisher:	College Park: American Physical Society
Abstract:	We present a unified treatment of three cases of quasi-exactly solvable problems, namely, charged particle moving in Coulomb and magnetic fields, for both the Schr\"odinger and the Klein-Gordon case, and the relative motion of two charged particles in an external oscillator potential. We show that all these cases are reducible to the same basic equation, which is quasi-exactly solvable owing to the existence of a hidden $sl_2$ algebraic structure. A systematic and unified algebraic solution to the basic equation using the method of factorization is given. Analytic expressions of the energies and the allowed frequencies for the three cases are given in terms of the roots of one and the same set of Bethe ansatz equations.
Relation:	Physical Review A (Atomic, Molecular, and Optical Physics) 63(6), pp.62105-62110
DOI:	10.1103/PhysRevA.63.062105
Appears in Collections:	[Graduate Institute & Department of Physics] Journal Article

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