Quasi-exactly Solvable Cases of the N-Dimensional Symmetric Quartic Anharmonic Oscillator  

作　　者：PAN Feng XIE Ming-Xia SHI Chang-Liang J.P.DRAAYER 潘峰;解明霞;史长亮;J.P.DRAAYER(Department of Physics,Liaoning Normal University,Dalian 116029;Department of Physics and Astronomy,Louisiana State University,Baton Rouge,LA 70803-4001,USA)

机构地区：[1]Department of Physics,Liaoning Normal University,Dalian 116029 [2]Department of Physics and Astronomy,Louisiana State University,Baton Rouge,LA 70803-4001,USA

出　　处：《Chinese Physics Letters》2012年第7期14-17,共4页中国物理快报（英文版）

基　　金：Support by the U.S.National Science Foundation(PHY-0500291&OCI-0904874);the Southeastern Universities Research Association,the Natural Science Foundation of China(11175078);the Doctoral Program Foundation of State Education Ministry of China(20102136110002);the LSU-LNNU joint research program(9961).

摘　　要：The O( N) invariant quartic anharmonic oscillator is shown to be exactly solvable if the interaction parameter satisfies special conditions.The problem is directly related to that of a quantum double well anharmonic oscillator in an external field.A finite dimensional matrix equation for the problem is constructed explicitly,along with analytical expressions for some excited states in the system.The corresponding Niven equations for determining the polynomial solutions for the problem are given.

关 键 词：field HARMONIC EXACTLY 

分 类 号：O17[理学—数学]