Question

If we have a wavefunction

$\Psi (\vec{r},0)=\sum_{n}^{ }c_{n}\Phi (\vec{r})$

Show using expectation values of the Hamiltonian that $c_{n}$ are amplitudes of probability and their square moduli $\left | c_{n} \right |^{2}$ give probability of measuring energy with eigenvalue $E_{n}$.

Answer 1

Grenen ware function & cor, o)= { an och) then expectation value of Hamiltonian. TH)= < (80)/H 1 4 (5,0) - 2 C C ( *)|H|db (S) = I laul². En . <H>= En vol so I len I ine probability of measuring enersy with eigenhalie en