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canbula
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Homework Statement
Consider an harmonic oscillator with time-dependent frequency as:
[itex]\omega (t)=\omega_0 * \exp^{- \lambda t}[/itex]
Find the time dependence of the ground state energy of this oscillator for [itex]\lambda << 1[/itex] situation.
Homework Equations
[itex]H=H_{0} + V(t)[/itex]
[itex]H_{0} = \frac{p^2}{2m} + \frac{1}{2} m \omega_{0}^{2} x^{2}[/itex]
and if we use the power series expansion for [itex]\lambda << 1[/itex] we get
[itex]V(t) = - \frac{1}{2} m \omega_{0}^2 \lambda t x^{2}[/itex]
The Attempt at a Solution
I know that I should use the time-dependent perturbation theory, but I am not good at it. So I need some help to solve this problem.
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