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Journal of Mathematical Physics / Volume 53 / Issue 1 / ARTICLES / Quantum Mechanics (General and Nonrelativistic)

J. Math. Phys. 53, 012102 (2012); http://dx.doi.org/10.1063/1.3676072 (8 pages)

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

Nuri Ünal

Department of Physics, Akdeniz University, P.K. 510, Antalya 07058, Turkey

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(Received 11 August 2011; accepted 15 December 2011; published online 6 January 2012)

In this study, we discuss the harmonic oscillator with the time-dependent frequency, ω(t), and the mass, M(t), by generalizing the holomorphic coordinates for the harmonic oscillator. In general cases, we solve the Schrödinger 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 [ω(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, ΔxΔp, is larger than minimum value; however, it is constant. We also discuss the classical equations of motion for the system.

© 2012 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. TIME-DEPENDENT HARMONIC OSCILLATORS
    1. Classical equations of motion
    2. Quantum equations
    3. The expectation values and uncertainties
  3. EXAMPLES
    1. Special case 1
    2. Special case 2
    3. Special case 3
  4. CONCLUSION

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KEYWORDS and PACS

Keywords

eigenvalues and eigenfunctions, harmonic oscillators, Riccati equations, Schrodinger equation

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3676072

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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