 #1
warhammer
 138
 28
 Homework Statement:

Consider a system in a state
ψ >=## frac{5/√50}*φ0 > +frac{4/√50}*φ1 > +frac{3/√50}*φ2 >##
where φ0 >, φ1 > and φ2 > are eigenstates of a harmonic oscillator
in ground, first and second excited state respectively.
(a) Find the average energy of this systemin the state ψ >.
(b) What is the probability that ψ > can be found in the state φ1 >?
 Relevant Equations:

Avg Energy E=P(j)*E(j) (where E(n)=ℏw(n+0.5)
P(1)=## frac{φ1ψ>^2/<ψψ > ##
Hi. I have attached a neatly done solution to the above question. I request someone to please check my solution and help me rectify any possible mistakes that I may have made.