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p828ps2

# p828ps2 - 1 √ 3 Y 1 θ φ B ψ r = R r √ 3 ± Y 1 1 θ...

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Physics 828: Problem Set 2 Dr. Stroud Due Wednesday, January 23 at 11:59:59 P. M. Each problem is worth 10 points unlesss otherwise specified. 1. Some properties of the Pauli spin matrices. (a). Verify Shankar, eq. (14.3.32). (b). Verify Shankar, eq. (14.3.38). (b). Verify Shankar, eq. (14.3.39). 2. Shankar, exercise 14.3.2. 3. Shankar, exercise 14.3.7. 4. (20 pts.) Conser a spin 1/2 particle. Call its spin S , its orbital angular momentum L , and its state vector | ψ ) . The two functions ψ ± ( r ) are defined by ψ ± ( r ) = ( r , ±| ψ ) . (These are the two components of the spinor wave function discussed in class.) Assume that ψ + ( r ) = R ( r ) bracketleftBigg Y 0 0 ( θ,φ ) + 1 3 Y 0 1 ( θ,φ
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Unformatted text preview: 1 √ 3 Y 1 ( θ, φ ) B ψ-( r ) = R ( r ) √ 3 ± Y 1 1 ( θ, φ ) − Y 1 ( θ, φ ) ² (1) where r , θ , and φ are the coordinates oF the particle and R ( r ) is a given Function oF r . (a). What condition must R(r) satisFy in order For | ψ a to be normalized? (b). S z is measured with the particle in state | ψ a . What results can be Found and with what probabilities? Same question For L z and then For S x . (c). A measurement oF L 2 with the particle in state | ψ a yielded zero. What state describes the particle just aFter this measurement? 1...
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