Consider a spin 1/2 particle. Call its spin S, its orbital angular momentum L and its...

Transcribed Image Text:

Consider a spin 1/2 particle. Call its spin S, its orbital angular momentum L and its state vector | >. The two functions (r) and _(r) are defined by: (r) = r₂ ± Assume that: | 4 ) .(r) = R(r) Y(0, p) + (ry[Y(G, + 7/3 109 (0.00)] R(r) v_(r) = RG [Y¦(0, ¢) — Y¦(0, q)] - where r, 0, 0, are the coordinates of the particle and R(r) is a given function of r. a. What condition must R(r) satisfy for | > to be normalized ? b. S. is measured with the particle in the state >. What results can be found, and with what probabilities? Same question for L., then for S. c. A measurement of L², with the particle in the state | >, yielded zero. What state describes the particle just after this measurement? Same question if the measurement of L² had given 2ħ². Q Consider a spin 1/2 particle. Call its spin S, its orbital angular momentum L and its state vector | >. The two functions (r) and _(r) are defined by: (r) = r₂ ± Assume that: | 4 ) .(r) = R(r) Y(0, p) + (ry[Y(G, + 7/3 109 (0.00)] R(r) v_(r) = RG [Y¦(0, ¢) — Y¦(0, q)] - where r, 0, 0, are the coordinates of the particle and R(r) is a given function of r. a. What condition must R(r) satisfy for | > to be normalized ? b. S. is measured with the particle in the state >. What results can be found, and with what probabilities? Same question for L., then for S. c. A measurement of L², with the particle in the state | >, yielded zero. What state describes the particle just after this measurement? Same question if the measurement of L² had given 2ħ². Q