HW08 & Solutions - ECE 306 Homework Set#8 Spring...

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ECE 306 Homework Set #8 Spring 2005 (Due Wednesday, April 6, 2005.) 1. A particle is known to be in a state such that L 2 = 2 Ñ 2 . It is also known that measurement of L z will yield the value + Ñ with the probability 1/3 and the value - Ñ with the probability 2/3. a. What is the normalized wave function Ψ ( θ , φ ), of this particle in terms of the ) , ( φ θ m l Y functions? b. What is the expectation value < L z >, of the z-component of the angular momentum of this particle? 2. The wave function of a particle of mass m moving in a potential well is, at a particular time t: 2 2 2 ) ( ) , , ( z y x e z y x z y x + + + + = α ψ a. Write Ψ in the spherical coordinate system, Ψ (r, θ , φ ) in normalized form
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