• Quantum states with continuous spectrum for a general time-dependent oscillator

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      https://www.ias.ac.in/article/fulltext/pram/065/02/0165-0176

    • Keywords

       

      Quantum states with continuous spectrum; time-dependent oscillator; invariant operator; unitary operator; propagator

    • Abstract

       

      We investigated quantum states with continuous spectrum for a general time-dependent oscillator using invariant operator and unitary transformation methods together. The form of the transformed invariant operator by a unitary operator is the same as the Hamiltonian of the simple harmonic oscillator:I’ = p2/2 +ω2q2/2. The fact thatω2 of the transformed invariant operator is constant enabled us to investigate the system separately for three cases, whereω2 > 0,ω2 < 0, andω2 = 0. The eigenstates of the system are discrete forω2 > 0. On the other hand, forω2 <− 0, the eigenstates are continuous. The time-dependent oscillators whose spectra of the wave function are continuous are not oscillatory. The wave function forω2 < 0 is expressed in terms of the parabolic cylinder function. We applied our theory to the driven harmonic oscillator with strongly pulsating mass.

    • Author Affiliations

       

      Jeong-Ryeol Choi1

      1. Department of New Material Science, Division of Natural Sciences, Sun Moon University, Asan - 336-708, Korea
    • Dates

       
  • Pramana – Journal of Physics | News

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