hw7 - PHYS 507 Homework VII(Fall'05 Assigned Wednesday Due...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
PHYS 507 Homework VII (Fall ’05) Assigned: November 30, 2005, Wednesday. Due: December 7, 2005, Wednesday, at 5:00 pm. 1. We have said in class that for any vector operator ~ V , the commutation relations [ J i ,V j ] = i ¯ h k ² ijk V k are satisfied where ~ J is the angular momentum. These rela- tions basically say that D ~ V E transforms like vectors under rotations. (a) Show that if ~ V and ~ U are vector operators then ~ W = ~ V × ~ U is also a vector operator. (Hint: These relations might be useful, k ² ijk ² nmk = δ in δ jm - δ im δ jn and V n U m - V m U n = ij ( δ in δ jm - δ im δ jn ) V i U j .) (b) What is ~ J × ~ J ? 2. Consider the state | j,m i which is a common eigenstate of J 2 and J z . Let ˆ n = cos φ ˆ x + sin φ ˆ y be a unit vector which is perpendicular to the z -axis, but otherwise arbitrary. The component of angular momentum along ˆ n is obviously J n = ˆ n · ~ J . Compute the following (a) What is h J n i and h J 2 n i ? Do these values depend on the angle
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/11/2012 for the course MATH 435 taught by Professor Starg during the Spring '11 term at Al Ahliyya Amman University.

Page1 / 2

hw7 - PHYS 507 Homework VII(Fall'05 Assigned Wednesday Due...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online