Recent content by wileecoyote

Please someone, help. I am so stuck.

What do you mean by the obvious way, I am not really sure what the obvious way to start this is.

yes at t=0 H(t) = ae^{-t/b} \left( \begin{array}{cc} 0 & 1 \\ 1 & 0 \end{array} \right)\

Homework Statement Given the Hamiltonian H(t) = \frac{P^2}{2m} + \frac{1}{2}mw^2X^2 + b(XP+PX) from some b>0. Find an annihilation operator a_b s.t. [a_b,a_b^{\dagger}]=1 and H = \hbar k (a_b^{\dagger}a_b+\frac{1}{2}) for some constant k. Hint: [P + aX,X]=[P,X], \forall a.Homework Equations...

Thanks, but how would I compute A(t). I'll give a little more detail. For this particular example, I am given that A = \left( \begin{array}{cc} 1 & 0 \\ 0 & -1 \end{array} \right) with eigenvalue 1 at t= 0. Since I've now got an expression for c_n(t) I can calculate |\phi (t)>, but what about...

Right so because of orthogonality each term where n \neq m will cancel leaving the left side as i \hbar \frac{d}{dt} c_n (t) but wouldn't the same have to happen to the right side making the equation i \hbar \frac{d}{dt} c_n (t) = f(t)E_n^0 c_n (t). Is that right? Also what about my second...

I'm not really sure how to deal with the sums, when I plug in and evaluate H^0I get i \hbar \frac{d}{dt} \sum\limits_{n=1}^N c_n (t)|E_n^0> = f(t) \sum\limits_{n=1}^N c_n (t) E_n^0 |E_n^0> and then if I act with a <E_n^0| it will simply cancel out the |E_n^0> (completeness relation), but then...

I'm working my way through some QM problems for self-study and this one has stumped me. Given the Hamiltonian as H(t) = f(t)H^0 where f(t) is a real function and H^0 is Hermitian with a complete set of eigenstates H^0|E_n^0> = E_n^0|E_n^0>. Time evolution is given by the Schrödinger equation i...