Symmetry of General Time-Dependent Harmonic Oscillator : Particles and Fields

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概要

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• The symmetries of various types of harmonic oscillators are determined. The conditions for the existence of these symmetries are derived. We explicitly give the algebra of the Lie symmetry group of the equation of motion together with the Noether invariants for the potential V(x) of the form x^k (k∈Z). It can be shown that non-trivial symmetry exists only for the case k=-2,0,1,2. Then we give explicitly the algebra of the Lie symmetry group of the equation of motion x^^^<・・>+2γ(t)x^^^・+Ω^2(t)x=K(x,t) and the Noether invariants for the cases K(x,t)=0 and K(x,t) ∝1/x^3. The case of the general time-dependence is easily obtained using the procedure we proposed previously. In quantum mechanics, we give explicit expressions of the symmetry of the Hamiltonian representing a harmonic oscillator including the case of general time-dependence.

• 理論物理学刊行会の論文
• 1997-04-25

著者

• Kanasugi Hirotaka

  Department Of Physics Tokyo Institute Of Technology

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