The matrix S r representing the component of spin angular momentum along an arbitrary direction r ^ . And the eigenvalues and normalized eigenspinors of S r .

Question

Want to see the full answer?

Answer 1

Question

Chapter 4.4, Problem 4.33P

To determine

The matrix Sr representing the component of spin angular momentum along an arbitrary direction r^. And the eigenvalues and normalized eigenspinors of Sr.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Students have asked these similar questions

3.20 Construct the matrix representations of the operators J, and J, for a spin 1 system, in the J. basis, spanned by the kets |+) = [1,1), 10) = 1,0), and -) = 1,-1). Use these matrices to find the three analogous eigenstates for each of the two operators J, and J, in terms of +), 10), and -).

Problem 3: Two-level system and density matrice Suppose a 2 x 2 matrix X (not necessarily Hermitian or unitary) is written as X = a000 + a.σ, where ao and ak, k = 1, 2, 3, are numbers, 0o = 1 is the identity matrix and o are the Pauli matrices. (a) How are ao and a related to tr(X) and tr(OX)? Obtain ao and ak in terms of the matrix elements Xij. Assume that ao, ak ER such that X is Hermitian and could be interpreted as a Hamiltonian, what are the eigenvalues of X?

Construct the 3D rotation ma- trices for rotations about the x-axis, y-axis, and z-axis by an angle o as described in I section 1.1.5. You should end up with three 3x3 matrices, one for each rotation axis. Demonstrate that your matrices do what they are supposed to do by considering >= 90 deg and applying them to an arbitrary vector A. Draw pictures to illustrate your reasoning.