Question on Intro QM pertaining to Harmonic Oscillator

  • Thread starter warhammer
  • Start date
  • #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{|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.

1654354474769.png
 

Answers and Replies

  • #2
kuruman
Science Advisor
Homework Helper
Insights Author
Gold Member
12,558
5,702
Last line ##4^2=16##. Other than that it looks good.
 
  • #3
warhammer
138
28
Last line ##4^2=16##. Other than that it looks good.
Ah yes! Sorry for that silly error, I noticed that now.

And thank you tons for your prompt guidance 🙏🏻
 

Suggested for: Question on Intro QM pertaining to Harmonic Oscillator

Replies
1
Views
268
  • Last Post
Replies
6
Views
604
Replies
6
Views
806
Replies
1
Views
547
  • Last Post
Replies
11
Views
318
Replies
7
Views
1K
  • Last Post
2
Replies
36
Views
1K
  • Last Post
Replies
4
Views
396
Top