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Question: consider a particle with mass m described by the hamilton...

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Consider a particle with mass m described by the Hamilton operator for a one-dimensional harmonic oscillator 2 рг 21 2 2m 2 The normalized eigenfunctions for Hare φη (x) with energies En-(n + 1) ha. At time t-Oth wavefunction of the particle is given by Now let H be a perturbation given by Where a is a constant. 1) Express H by the step-operators a+ and a_. 2) Show that the first-order energy correction in α is 0 for the nth eigenstate. 3) Calculate the second order energy correction for the nth eigenstate

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