Question

1. (50 points) Consider the particle in a one-dimensional box (0 s x S L). Assume a term is added to the Hamiltonian of the form: πχ V(x)g sin Sketch the potential and the expected eigenfunction (small g). In the limit of small g, find the second order correction to the ground state energy 2. (50 points) For a diatomic molecule rotating in free space, the Hamiltonian may be written: 12 21 Where L is the total angular momentum operator, and I is a constant (the moment of inertia). Remember (0 eigenfunctions for the θ π; 0 φ 1 state are: 2π) and d-sin θ d θ d φ. The normalized

Answer 1

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21

Integratelsin!π k LI sin|π LI SinIn π LI , {х, О, L] // Fullsimplify Integrate Isin!π k LI sin!π LI sinl π LI , {x, o, L] // Fullsimplify 2L (-1+cos [ k π ] )