Introduction and Applications of a Generalized Intermediate Entangled State Representation

庞乾骏

Wen-Jian Yu, Hong‐Chun Yuan, Ji‐Suo Wang

Pang Qian-Jun

We introduce a generalized intermediate entangled state representation |β⟩ Λ to study the energy spectrum of an electron in a uniform magnetic field and a harmonic potential through algebraic calculation. We find that the degeneracy of the energy levels is disappeared due to the existence of the additional potential. We make it clear that the eigenfunction is just the expression of eigenvector, defined in n Fock space, in |β⟩ Λ representation.

Gang Ren, Jian-guo Ma, Jian-ming Du +1 more

Qin Guo, Liying Jiang, Cunjin Liu +2 more

By combining the beam splitter and the Fresnel transform, a protocol is proposed to generate a new entangled state representation, called the intermediate coherent-entangled state (ICES) representation. The properties, such as eigenvalue equation, completeness relation and orthogonal relation, are investigated. The conjugate state representation of the ICES and the Schmidt decomposing of the ICES are also discussed. As applications, a new squeezing operator and some operator identities by using the ICES are obtained.

Pang Qian-Jun

We present a general discussion on the eigenstate problem of a bipartite complicated-coupled-oscillator system. By use of a generalized intermediate entangled state representation, the eigenvalue and eigenfunction of Hamiltonian are analytically obtained. As its application, we obtain the energy spectrum for two special situations of Hamiltonian.