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d) Show that any two n(0) and m(0) with m # n satisfy V*(0)Wm(0)d0 = 0 %3D

d) Show that any two n(0) and m(0) with m # n satisfy V*(0)Wm(0)d0 = 0 %3D

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Question d only. Please do it step by step and show how you do the integration for complex exponentials

2. The quantum states of a particle moving freely in a circle of radius r are described by bn (0) C'ewno where C is a constant, 0 denotes angle, n = 0, ±1,±2, ... is an integer identifying the quantum state of the particle, and wn is constant for a given n. a) Show that ,(0) satisfies d02 b) Find w, such that Wn(0 +27) = n(0) c) Find the value of C such that 27T | In (0)l°d0 = 1 d) Show that any two v,(0) and m(0) with m +n satisfy | (0)bm (0)d0 = 0
Transcribed Image Text:2. The quantum states of a particle moving freely in a circle of radius r are described by bn (0) C'ewno where C is a constant, 0 denotes angle, n = 0, ±1,±2, ... is an integer identifying the quantum state of the particle, and wn is constant for a given n. a) Show that ,(0) satisfies d02 b) Find w, such that Wn(0 +27) = n(0) c) Find the value of C such that 27T | In (0)l°d0 = 1 d) Show that any two v,(0) and m(0) with m +n satisfy | (0)bm (0)d0 = 0
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