(Solved): 60 Typing out the answer preferably Problem 6 Suppose you have a general state vector [n) whi ...

60 Typing out the answer preferably

Problem 6 Suppose you have a general state vector [n) which is an eigenvector of the Hamiltonian H for a particle in a 1-dimensional box with size a. The eigenvalues are En = 2m2, and the associated eigenvectors form a basis for the corresponding Hilbert space. = (a) (1 pts) What is H |n) equal to? (b) (1 pts) What is Hm) equal to? (c) (1 pts) What is (m| H |n) equal to? (d) (1 pts) What is (n| H |n) equal to? (e) (2 pts) From the two last points, write down the Hamiltonian as a matrix, whose matrix components are Hmn = (m| H |n). Do not just write En for each entry, but write down the full expression of the energy.