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 o...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.展开更多
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)+1 种基金the Doctoral Program Foundation of State Education Ministry of China(20102136110002)the LSU-LNNU joint research program(9961).
文摘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.