The coherent states of harmonic oscillator with complex frequency (Q805321)

The model of the harmonic oscillator with complex frequency is very valuable for the study of the dissipation theory in physics. The model of the dissipation and nuclear friction can be seen as particular cases of the harmonic oscillator with complex frequency. Because of the complex frequency, the eigenvalues of the energy are complex numbers and the partition functions of Boltzman and Helmholtz's free energy are complex functions, the imaginary part of the free energy describes the metastable states. In this note are introduced the usual commutation rules satisfying the complex annihilation and creation operators. As two special examples, we have obtained the wave functions for the coherent states of the positive and the inverted harmonic oscillators.