Exact Quantum Theory of the Harmonic Oscillator with the Classical Solution in the Form of Mathieu Functions
Exact Quantum Theory of the Harmonic Oscillator with the Classical Solution in the Form of Mathieu Functions
- 주제(키워드) Harmonic oscillator , Exact theory , Harmonic oscillator , Exact theory
- 발행기관 한국물리학회
- 발행년도 2002
- 총서유형 Journal
- UCI G704-000411.2002.40.6.014
- KCI ID ART000882014
초록/요약
Using the dynamical invariant operator method, we obtain the exact wave function, uncertainty relation, and energy eigenvalues for the harmonic oscillator with the classical equation of motion in the form of Mathieu functions. The probability density varies as a function of position, but is almost constant in time. The uncertainty relations satisfy the minimum uncertainty, and the energy eigenvalues oscillate slowly or rapidly depending on the frequency. The quantum and classical energies oscillate in a similar fashion with respect to frequency and time.
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