Discuss whether or not you expect this perturbing potential to mix states with

Discuss whether or not you expect this perturbing

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Discuss whether or not you expect this perturbing potential to mix states with even and odd quantum numbers, explaining why. (d) Evaluate the effect of the perturbation on the ground state wavefunction to first order by working out the coupling matrix elements. Compare the values against your best results from the previous problem. 5. Let’s regard the mighty methane molecule (CH 4 ) as a rigid tetrahedron, with the C atom at its center, and CH bond lengths of 1.1 Å. (a) Find the position of the center of mass of the molecule. (c) What is the moment of inertia about an axis which is one of the CH bonds? (d) Show that the moment of inertia about either of the two perpendicular axes is the same. Thus the moment of inertia is independent of the choice of axes in methane, and it is a spherical top. (e) Calculate the energies of the first 3 energy levels ( l =0,1,2), and their energy differences. In what part of the electromagnetic spectrum do they lie? (f) Would you expect to observe transitions between these energy levels when radiation of the appropriate frequency is applied to the methane molecule? Why or why not?
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  • Summer '16
  • Alistair Sinclair

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