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1988•Progress of Theoretical PhysicsOpen access

Semiclassical Description of Bound State Wave Functions for Integrable Systems: -- R(4) Model --

T. Suzuki, Y. Mizobuchi

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Abstract

Semiclassical wave functions of bound states are constructed for an integrable model having R(4) ≃SU(2)⊗SU(2) symmetry. Each eigenstate is expressed as an integral of generalized coherent states over a quantized torus, which satisfies a standard Einstein-Brillouin-Keller quantization condition. Obtained wave functions as well as transition rates are compared with those of exact solutions calculated via diagonalization. Semiclassical and exact results show a close correspondence over a broad range of the parameters in the model.

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Semiclassical wave functions of bound states are constructed for an integrable model having R(4) ≃SU(2)⊗SU(2) symmetry. Each eigenstate is expressed as an integral of generalized coherent states over a quantized torus, which satisfies a standard Einstein-Brillouin-Keller quantization condition. Obtained wave functions as well as transition rates are compared with those of exact solutions calculated via diagonalization. Semiclassical and exact results show a close correspondence over a broad range of the parameters in the model.

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Available abstract

Semiclassical wave functions of bound states are constructed for an integrable model having R(4) ≃SU(2)⊗SU(2) symmetry. Each eigenstate is expressed as an integral of generalized coherent states over a quantized torus, which satisfies a standard Einstein-Brillouin-Keller quantization condition. Obtained wave functions as well as transition rates are compared with those of exact solutions calculated via diagonalization. Semiclassical and exact results show a close correspondence over a broad range of the parameters in the model.

Key concepts: Semiclassical physics, Physics, Integrable system, Mathematical physics, Bound state, Quantization (signal processing), Torus, Wave function

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