(h) Consider a harmonic oscillator that is split into a double well potential. Consider only the...

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(h) Consider a harmonic oscillator that is split into a double well potential. Consider only the v = 2 wave function at the energy shown. V(x) x-> v=2 v = 1 v=0 original potential i. Using principles from perturbation theory, suggest what happens to the wave function and its energy due to the change in the potential, thinking physically about the perturbation to the original potential. ii. Using principles from variational theory, what other harmonic oscillator wave function would you add to the usual Yv=2 wave function to accomplish the required shift in energy? Why? Try to preserve the symmetry of the v = 2 state. (h) Consider a harmonic oscillator that is split into a double well potential. Consider only the v = 2 wave function at the energy shown. V(x) x-> v=2 v = 1 v=0 original potential i. Using principles from perturbation theory, suggest what happens to the wave function and its energy due to the change in the potential, thinking physically about the perturbation to the original potential. ii. Using principles from variational theory, what other harmonic oscillator wave function would you add to the usual Yv=2 wave function to accomplish the required shift in energy? Why? Try to preserve the symmetry of the v = 2 state.