Info Test Survey Multiple choice question, more than one right answer The Hamiltonian of a free particle is \[ H = {1\over 2m} \sum^3_{i-1} p^2_i.\label{2solp1e1}\] The Heisenberg equations of motion for \(p_i\) and \(x_j\) are \[{dp_j\over dt} = {1\over i\hbar} [p_j, H] = 0,\label{2solp1e2}\] \[ {dx_j\over dt} = {1\over i\hbar}[x_j, H] = {1\over 2i\hbar m}\sum^3_{i=1}[x_j, p^2_j] = {p_i\over m},\label{2solp1e3}\] From Eq. {2solp1e2} we have \(p_j(t) - p_j(0)\). Hence the solution of Eq.{2solp1e2} is \[ x_j(t) = x_j(0) + {p_j(0)\over m}t.\label{2solp1e4}\] Since \([x_i, p_j] = i\hbar\delta_{ij}\) we obtain \[ [x_j(t), x_i(0)] = -{i\hbar t\over m}\delta_{ij}.\label{2solp1e5}\] \setcounter{equation}{0} option 1 option 2 option 3 option 4 Your student number Comments Questions about your habits. Strongly disagree Disagree Neither agree nor disagree Agree Strongly agree You are a self conscious student. You like to study all the time. You never go to parties. Multiple choice question one right answer line 1 line 2 line 3 line 4 formula question value1 value2 value3 Are you a human?
