非对易相空间三模坐标动量耦合谐振子的能谱

本文用不变本征算符方法研究非对易相空间中三模坐标动量耦合谐振子的能谱,分别得到了非耦合和坐标动量耦合两种情况下谐振子能谱的解析解,其中包括受非对易参数θ和φ影响的解λ0,1和λ1,1,以及不受非对易参数θ和φ影响的解λ0,2和λ1,2.然后,分析了两类耦合参数κ和η对三模坐标动量耦合谐振子能谱的影响.结果发现,耦合参数κ和η对λ1,1的影响是相同的,且当κ=η时,耦合系数κ和η对λ1,1是没有影响的.

Energy spectrum of three-mode coordinate-momentum coupling harmonic oscillator in non-commutative phase space

In non-commutative phase space,energy spectrum of three-mode coordinate-momentum coupling harmonic oscillator is analyzed by using the invariant eigen-operator method.The explicit expressions for two kinds of three-mode harmonic oscillators:no coupling and coordinate-momentum coupling are obtained.Some expressions λ0,1 and λ1,1 have be connected with non-commutative parameters θ and φ,others λ0,2 and λ1,2 do not.It is discussed about the effect of coupling parameters on energy spectrum of three-mode coordinate-momentum coupling harmonic oscillator.The results show that the coupling parametersκandηhave the similar effect on the λ1,1.Furthermore,they do not have any effect on the λ1,1 whenκandηare equal.