2 Working with spin ½ angular momentum for a 2 particle system There are

# 2 working with spin ½ angular momentum for a 2

• 4

This preview shows page 1 - 3 out of 4 pages.

2. Working with spin ½ angular momentum for a 2-particle system. There are several ways to find the eigenvalues and eigenvectors of a system with two spins. Here you will find the eigenvalues and eigenvectors by constructing the appropriate matrices. In question 1 above, you worked with the 2 × 2 Pauli matrices that describe spin ½ in the basis α and β . Now it is time to construct the 4 × 4 matrices which describe the spin of 2 electrons in the basis formed by αα , βα , αβ , ββ (often called the tensor product basis because it is the made from the product of the two functions for spin 1 with the two functions for spin 2) . (a) Use the 2 × 2 Pauli matrices to evaluate the 4 × 4 matrix describing ˆ S z = ˆ s z 1 + ˆ s z 2 . What are its eigenvalues and their degeneracies? (b) Use the 2 × 2 Pauli matrices to evaluate the 4 × 4 matrix describing ˆ S x = ˆ s x 1 + ˆ s x 2 (c) Use the 2 × 2 Pauli matrices to evaluate the 4 × 4 matrix describing ˆ S y = ˆ s y 1 + ˆ s y 2 (d) Use your answers to the above to make the 4 × 4 matrix describing ˆ S 2 = ˆ S ˆ S

Subscribe to view the full document.

(e) Find the eigenvalues of ˆ S 2 = ˆ S ˆ S and the common eigenvectors of ˆ S 2 = ˆ S ˆ S and ˆ S z = ˆ s z 1 + ˆ s z 2 . You should find a singlet and the three components of a triplet, as claimed in lecture!
• Summer '16
• Alistair Sinclair
• Matrices, Eigenvalue, eigenvector and eigenspace, Use python, HFCO

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern

Ask Expert Tutors You can ask 0 bonus questions You can ask 0 questions (0 expire soon) You can ask 0 questions (will expire )
Answers in as fast as 15 minutes