Authors: Eun Ji Jang, Jihun Cha, Young Kyu Lee, Won Sang Chung
In this paper we extend the so-called dual or mirror image formalism and Caldirola's- Kanai's formalism for damped harmonic oscillator to the case that both frictional coefficient and time-dependent frequency depend on time explicitly. As an solvable example, we consider the case that frictional coefficient $ \ga (t) = \frac{ \ga_0}{1 + q t} , (q > 0 )$ and angular frequency function $ w(t) = \frac{ w_0}{ 1 + q t } $. For this choice, we construct the quantum harmonic Hamiltonian and express it in terms of $su(2)$ algebra generators. Using the exact invariant for the Hamiltonian and its unitary transform, we solve the time-dependent Schro\"dinger equation with time-dependent frictional coefficient and time-dependent frequency.
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[v1] 2015-10-01 18:03:19
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