Quasi-coherent states for harmonic oscillator with time-dependent parameters

Unal N.

JOURNAL OF MATHEMATICAL PHYSICS, cilt.53, sa.1, 2012 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 53 Sayı: 1
  • Basım Tarihi: 2012
  • Doi Numarası: 10.1063/1.3676072
  • Dergi Adı: JOURNAL OF MATHEMATICAL PHYSICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Akdeniz Üniversitesi Adresli: Hayır

Özet

In this study, we discuss the harmonic oscillator with the time-dependent frequency, omega(t), and the mass, M(t), by generalizing the holomorphic coordinates for the harmonic oscillator. In general cases, we solve the Schrodinger equation by reducing it into the Riccati equation and discuss the uncertainties for the quasi-coherent states of the time-dependent harmonic oscillator. In special cases, we find the following results: First, for a time-dependent harmonic oscillator, if [omega(t) M(t)] is constant, then the coherent states will evolve as the coherent states. Second, for the driven harmonic oscillator, the coherent states will evolve as the coherent states with new eigenvalues. Third, we derive quasi-coherent states for the Caldirola-Kanai Hamiltonian and show that the product of uncertainties, Delta x Delta p, is larger than minimum value; however, it is constant. We also discuss the classical equations of motion for the system. (C) 2012 American Institute of Physics. [doi: 10.1063/1.3676072]