# Question: a write down the timeindependent schrdinger equation for psix b...

###### Question details

a) Write down the time-independent Schrödinger equation for psi(x).

b) Write down the Hamiltonian operator **H in terms of the
ladder operators** a+ and a_. (You do not need to derive
it)

c) Use your result from (b) to **calculate**
a+a_psi_n(x). Give your answer in terms of n, psi_n(x), psi_n+1(x),
and psi_n-1(x).

d) **Normalize psi(x).**

e) If you were to measure the energy of the particle, what
**values** *could* you obtain, and with what
**probability**? (You should be able to write down the
answer without any further calculations).

f) Calculate the **expectation value of the
Hamiltonian,** <H>. Is your result consistent with
part (e)?