homework11solutions.pdf - Physics 217 Homework 11 1 L~1 =...

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Physics 217 Homework 11 1. L 1 = r 1 × p 1 = 1 . 2 × 10 - 5 kg · m 2 /s . This is the angular momentum due to one ball, the total angular momentum is 2 times this number. We also know that L = l ( l +1) ¯ h . Equating these two we get l = 2 . 37 × 10 29 . There are 2 l + 1 = 4 . 74 × 10 29 possible values of m l . 2. Y 11 = - 1 2 3 2 π sin θe . Plugging this into the two given equations and having fun with some algebra you see that the equations are satisfied. 3. (a) The wave function of the ground state is given by ψ = 1 π 1 a 0 3 / 2 e - r/a 0 and the potential is given by V ( r ) = - e 2 4 π 0 r . Using these two quantities you find that the expectation value of the potential energy is ¯ V = - 27 . 2eV. (b) E 1 = - 13 . 6 1 2 = - 13 . 6eV=
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