(a) Show that the sum of two hermitian operators is hermitian.(b) Suppose  is hermitian, a...

(a) Show that the sum of two hermitian operators is hermitian.

(b) Suppose  is hermitian, and α is a complex number. Under what condition (on α) is α  hermitian?

(c) When is the product of two hermitian operators hermitian?

(d) Show that the position operator ( = x) and the hamiltonian operator ( = −(h2/2m)d2/dx2 + V(x)) are hermitian.