Question

5. A quantum system is described by the one-dimensional Hamiltonian (in units here 1) d2 dz2 Notice that this Hamiltonian has the potential energy of x2 (we will soon see that this Hamil tonian describes a good model of molecular vibration). Let us consider the two wavefunctions (a) Show that h(z) and 2(z) are eigenfunctions of this Hamiltonian and find their corre- sponding eigenvalues. (b) Find the constants Ai and A2 that normalize the wavefunctions i(x) and 2(x). Use the equation sheet posted on the LON-CAPA site to find the correct integral formulas. The integration limits should be from -oo to +oo. (c) Evaluate the expectation value (x) for i and . You will find that you don't need to evaluate any integrals, although you may do so.

PLEASE WRITE AS CLEAR AS POSSIBLE  

Answer 1

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