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College Physics

Double-mode integral form projection operator and its application

Xing-Lei Xu

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

A double-mode integral form projection unitary operator is introduced. Using the technique of integration within an ordered product (IWOP) of operators, the transformation character of the integral form projection operator is studied. The Hamiltonian of double-mode quantum harmonic oscillator system with kinetic coupling is diagonalized by virtue of the integral form projection operator, and then the eigenenergy and eigenfunction of the system are accurately solved. Finally the particular case is discussed.

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College Physics•Jan 1, 2009•0 citations
A double-mode integral form projection unitary operator is introduced. Using the technique of integration within an ordered product (IWOP) of operators, the transformation character of the integral form projection operator is studied. The Hamiltonian of double-mode quantum harmonic oscillator system with kinetic coupling is diagonalized by virtue of the integral form projection operator, and then the eigenenergy and eigenfunction of the system are accurately solved. Finally the particular case is discussed.
A two-mode integral form projection unitary operator is introduced. Using the technique of integration within an ordered product （IWOP） of operators, the transformation property of the integral form projection operator is studied, and its normal ordered expression is derived. Then the Hamiltonian of two-mode quantum harmonic oscillator system with coordinate-momentum coupling is diagonalized by virtue of the integral form projection operator, there by the eigenenergy and eigenfunction of the system are exactly solved. Lastly, a special case is discussed.
A unitary transformation matrix, n linear-composite coordinate operators and n linear-composite momentum operators are constructed for an n-particle system, and the complete and orthonormal common eigenvectors of the multi-mode linear composite momentum operators are examined by virtue of the technique of integration within an ordered product of operators. The multi-mode linear composite momentum representation is proposed, and its application to a general two-mode forced quantum harmonic oscillator system with kinetic coupling is presented for solving some dynamic problems.
In order to solve dynamic problems of double non-identical quantum harmonic oscillators with interaction potential and movement coupling, the new two mode composite coordinate representation |η1，η2〉 is proposed by the technique of integration within an ordered product of operators. The two mode squeezing operator U is constructed, and its characteristics are analyzed. Moreover, its application to double non-identical quantum harmonic oscillators with interaction potential and movement coupling is presented for solving some the dynamic problems. Approach of solving some the dynamic problems involving complicated quantum harmonic oscillators is proposed.
In view of a recent paper [F. Michelot, Phys. Rev. A 45, 4271 (1992)] tackling the Hamiltonian of an arbitrary number of harmonically coupled oscillators, we present a coordinate representation of the unitary operator that can diagonalize the Hamiltonian. The normally ordered form of the unitary operator, which manifestly connects two Fock spaces associated with the uncoupled and coupled oscillators, is also derived by virtue of the technique of integration within an ordered product of operators.