- #1

warhammer

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- 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{|φ1|ψ>^2/<ψ|ψ > ##

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.