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Unformatted text preview: mentum. (b) What are the normalized eigenfunctions for this system? What is the de-generacy of the n th energy level? 5. (a) Find h r i and h r 2 i for an electron in the ground state of hydrogen. Express your answers in terms of the Bohr radius. (b) Find h x i and h x 2 i for an electron in the ground state of hydrogen. (c) Find h x 2 i in the state n = 2, l = 1, m = 1. 6. Suppose we perturb the inﬁnite cubical potential well of side a by putting a delta function “bump” at the point ( a/ 4 ,a/ 2 , 3 a/ 4): H = a 3 V δ ( x-a/ 4) δ ( y-a/ 2) δ ( z-3 a/ 4) . Find the energy (up tp second-order corrections) and eigenfunction (up to ﬁrst-order corrections) of the ground state and the (triply degenerate) ﬁrst excited states. —— End ——...
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- Spring '11