- #1

- 325

- 3

_{a}is the probability of the system being in the state [tex] |\Psi_a(t)\rangle [/tex]

I am asked to first show that the trace [tex] Tr(\rho) = 1 [/tex] and that the expectation value of some operator K is [tex] \langle K \rangle = Tr(\rho K) [/tex], which was fairly straightforward. Then the part I am having problems with is that is asks me to "show that the equation of motion is [tex] i\hbar\frac{\partial \rho(t)}{\partial t} = [H,\rho (t)] [/tex] ".

I am told nothing about what situation this "equation of motion" might apply to. This is literally everything the question tells me and I have never been asked to do this before in a quantum sense. The only kind of equation of motion I have ever had to set up was in a classical sense like, say, a damped spring, say [tex] m\frac{d^2x}{dt^2} = -c\frac{dx}{dt} - kx [/tex] and clearly this is done in terms of forces, which don't seem to get used in quantum mechanics.

So in short, I have no idea what I am supposed to make of this, or what use calculating that trace and expectation value was, if that has any relevance. Any suggestions on how to approach this?

Thanks.