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The hamiltonian of a half spin particle

  1. May 18, 2009 #1
    1. The problem statement, all variables and given/known data

    The Hamiltonian for a spin-half particle is

    H = 2a/ħ (Sx + Sy)

    where a is a positive constant and Sx , Sy are the x and y components of the spin. Initially (at time t=0) the particle is in the state

    |ψ> = (1/√2) (|↑>+|↓>)

    where up and down arrows denote eigenstates of the z component of the spin.

    a) Calculate the expectation value of the energy <E> and of the three components of the spin <Sx>, <Sy> and <Sz> at t=0.
    b) What is the probability that a measurement of the x component of the spin at t=0 will give the value +ħ/2 ?
    c) Find the eigenstates and eigenvalues of the Hamiltonian.
    d) Find the state |ψ(t)> at a later time t.
    e) What is the probability that a measurement of the x component of the spin at time t will give the value +ħ/2 ?

    This is a practice exam question that I'm using to prepare for my final. Any help would be greatly appreciated. It's tough being the only Mechanical Engineer in a group full of physics majors. Thanks to anyone who can help me out.



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. May 18, 2009 #2
    What's your first step? Any relevant equations?
     
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