The variety of quantum state of transfers particle and unitary transformation matrix of acceptant are calculated in theory by four Bell radix.

In this paper,we presented a succinct method to obtain the unitary matrix in the representation transformation by the theorem form,gave the reasonable demonstration,and simultaneously confirmed the theorem accuracy by a concrete example.

Constructing a unitary matrix for transformation of coordinates by means of quadratic form theory,the Hamiltonian of the 3D coordinate-momentum coupling harmonic oscillator is transformed into diagonalmatrix,it not only offer a general mathematic method for solving this kind of problems,but also have an active effect upon upgrading students ability to solve physics problems by mathematical theory.

By utilizing the unitary transformation such as the rotational transformation in Schwinger angular momentum representation,Bogoliubov transformation and the squeezed transformation,the two-body interacting Hamiltonian in the form of H∧_k=A_1a~+_ka_k+A_2b~+_kb_k+(Ba~+_kb~+_k+B~*a_kb_k)+(Ca~+_kb_k+C~*b~+_ka_k)is diagonalized.

The Hamiltonian of the system was diagonalized by unitary transformation to obtain the eigenenergy spectra of the circuit.

We find that when the channels are nonmaximally (entangled) states by introducing an ancillary qubit and constructing an unitary transformation properly,teleportation of two-particle entangled state can be implemented with certain probability.

In thisarticle,theoperator \$Q,\$characterizing the semiunitary transformation relating the partner Hamiltonians,proposed in Refs and is structured for some circumstances in SSQM.