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Journal of Physics A Mathematical and General

Squeezing in the triatomic linear molecule model revealed by virtue of the IWOP technique

Fan Hong-Yi

Published Jan 7, 1993• 11 citations
Publisher

Abstract

For a typical triatomic linear molecule with different atomic masses one finds a unitary operator which is closely related to squeezing transformations caused by frequency jumps. The coordinate representation of the unitary operator is identified, which provides an alternative approach for calculating the wavefunction of internal motion of the molecule. The author also shows that the unitary operator is equivalent to a two-mode squeezing-rotating combination operator multiplied from the right by two single-mode squeezing operators. The discussion is mainly based on the technique of integration within an ordered product (IWOP) of operators.

DOI
10.1088/0305-4470/26/1/016

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Communications in Theoretical Physics•Oct 30, 1999•1 citation
For a typical triatomic linear molecule with different atomic masses one finds a unitary operator which is closely related to squeezing transformations caused by frequency jumps. The coordinate representation of the unitary operator is identified, which provides an alternative approach for calculating the wavefunction of internal motion of the molecule. The author also shows that the unitary operator is equivalent to a two-mode squeezing-rotating combination operator multiplied from the right by two single-mode squeezing operators. The discussion is mainly based on the technique of integration within an ordered product (IWOP) of operators.
We present the continuous state vector of the total coordinate of multi-particle and the state vector of their total momentum, respectively, which possess completeness relation in multi-mode Fock space by virtue of the integration within an order product (IWOP) technique. We also calculate the transition from classical transformation of variables in the states to quantum unitary operator, deduce a new multi-mode squeezing operator, and discuss its squeezing effect. In progress, it indicates that the IWOP technique provides a convenient way to construct new representation in quantum mechanics.
We find the unitary operator for diagonalizing the Hamiltonian of a triatomic linear molecule. The unitary operator is expressed in a coordinate representation that brings convenience for deriving the density matrix \ensuremath{\rho}(x1{\mathrm{x}}_{1}x1​,x2{\mathrm{x}}_{2}x2​,x3{\mathrm{x}}_{3}x3​;${\mathrm{x}}_{1}^{\ensuremath{'}}$,${\mathrm{x}}_{2}^{\ensuremath{'}}$,${\mathrm{x}}_{3}^{\ensuremath{'}}$,\ensuremath{\beta}). The unitary transformation approach is simple because the derivation can be reduced to the calculation of two independent harmonic-oscillator density matrices and one free-particle density matrix. The average of the potential energy and the kinetic of the molecule is calculated by using the density matrix.