{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ps4 - Physics 212 Spring 2010 Problem Set 4 1 C-TDL Ch X...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Physics 212 Spring 2010 Problem Set 4 1. C-TDL Ch. X problem 1 2. C-TDL Ch. X problem 3 3. Show, using a plane wave as your original eigenstate, that the momentum operator “generates” a translation in space. Prove that a unitary operator U may be written in terms of a Hermitian operator G , where U = exp( iθG ), where θ is arbitrary. 4. “Adding” l = 1 with s = 1 / 2: Use raising and lowering operators as well as orthogonality to express the combined basis states in terms of the individual basis states | l = 1 , m l , s = 1 / 2 , m s i . 5. Shankar 12.5.7 6. Sakurai Ch. 3 Problem 8 (Sakurai is on reserve in the library if you want to see the problems in their original form. If that is inconvenient, they are reproduced here): Consider a sequence of Euler rotations represented by D 1 / 2 ( α, β, γ ) = exp ( - 3 α 2 ) exp ( - 2 β 2 ) exp ( - 3 γ 2 ) . [The (1 / 2) superscript on D means that we are in a spin 1/2 system, so the matrices are the Pauli matrices.] Because of the group properties of rotations, we expect that this sequence of operations is equivalent to a single rotation about some axis by an angle θ . Find θ .
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern