By virtue of the technique of integration within an ordered product of operators, we derive the normal ordering expansion of a one- and two-mode combination squeezing operator for two harmonic oscillators with coordin...By virtue of the technique of integration within an ordered product of operators, we derive the normal ordering expansion of a one- and two-mode combination squeezing operator for two harmonic oscillators with coordinate- momentum coupling. It turns out that this squeezing operator just diagonalizes the Hamiltonian H=p^21/2m1＋m1ω^21x^21/2＋p^222m2＋m2ω^22x^22/2-λx2p1 so its ground state is a one- and two-mode combination squeezed state. Quantum fluctuation in the ground state is calculated.展开更多
Usually the Virial theorem,which can be derived from the Feynman-Hellmann theorem,applies to Hamil-tonians without coordinates-momentum coupling.In this paper we discuss when there are such kind of couplings inHamilto...Usually the Virial theorem,which can be derived from the Feynman-Hellmann theorem,applies to Hamil-tonians without coordinates-momentum coupling.In this paper we discuss when there are such kind of couplings inHamiltonians then how the Virial theorem should be modified.We also discuss the energy contribution arising from thecoordinates-momentum coupling for a definite energy level.展开更多
The generalized Virial theorem for mixed state, derived from the generalized Hellmann Feynman theorem, only applies to Hamiltonians in which potential of coordinates is separate from momentum energy term. In this pape...The generalized Virial theorem for mixed state, derived from the generalized Hellmann Feynman theorem, only applies to Hamiltonians in which potential of coordinates is separate from momentum energy term. In this paper we discuss Virial theorem for mixed state for some Hamiltonians with coordinate-momentum couplings in order to know their contributions to internal energy.展开更多
文摘By virtue of the technique of integration within an ordered product of operators, we derive the normal ordering expansion of a one- and two-mode combination squeezing operator for two harmonic oscillators with coordinate- momentum coupling. It turns out that this squeezing operator just diagonalizes the Hamiltonian H=p^21/2m1＋m1ω^21x^21/2＋p^222m2＋m2ω^22x^22/2-λx2p1 so its ground state is a one- and two-mode combination squeezed state. Quantum fluctuation in the ground state is calculated.
基金the Specialized Research Fund for the Doctorial Progress of Higher Education of China under Grant No.20070358009
文摘Usually the Virial theorem,which can be derived from the Feynman-Hellmann theorem,applies to Hamil-tonians without coordinates-momentum coupling.In this paper we discuss when there are such kind of couplings inHamiltonians then how the Virial theorem should be modified.We also discuss the energy contribution arising from thecoordinates-momentum coupling for a definite energy level.
文摘The generalized Virial theorem for mixed state, derived from the generalized Hellmann Feynman theorem, only applies to Hamiltonians in which potential of coordinates is separate from momentum energy term. In this paper we discuss Virial theorem for mixed state for some Hamiltonians with coordinate-momentum couplings in order to know their contributions to internal energy.
