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  3. 3 harmonic oscillator 25 marks consider a linear harmonic oscillator...

Question: 3 harmonic oscillator 25 marks consider a linear harmonic oscillator...

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3) Harmonic Oscillator (25 marks): Consider a linear harmonic oscillator with the solution de- fined by the ladder operators a and at defined in class. Use the number basis In) to do the following. a) Construct a linear combination of l0) and 1) to form a state lu) such that (X)is as large as possible. b) Suppose that the oscillator is in the state constructed in a) at time t-0. Write an expression to de- scribe the time dependence of this state state for t > 0, Evaluate the expectation value (t(이지ψ(t)) as a function of time for t 0 e) Defining (Ar)x)) (Xl(). Calculate (Ar)2.

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