A briefly question: what's the "physical meaning" of the off-diagonal elements of Hamiltonian matrix? Such as an Hamiltonian Matraix looks like: $$\hat H = \begin{pmatrix} E_{11} & E_{12} \\ E_{21} & E_{22} \end{pmatrix}$$ My teacher told me such a matrix element : $$E_{21}=\langle2|\hat H|1\rang...

In the arrangement shown in figure, the ends P and Q of an inextensible string move downwards with uniform speed u. Pulleys A and B are fixed. The mass M moves upwards with what speed? I tried to solve this problem with the following way- Let the upward speed of the mass M be x. Then, $$x=\sqrt{...