Question on Intro QM pertaining to Harmonic Oscillator

Thread starter warhammer
Start date Jun 4, 2022
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Harmonic Harmonic oscillator Intro Oscillator Qm

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The discussion revolves around a solution to a question on Intro QM related to the Harmonic Oscillator. The original poster seeks feedback on their solution and requests help in identifying any mistakes. A participant points out a specific error regarding the calculation of 4^2, confirming it equals 16. The original poster acknowledges the mistake and expresses gratitude for the assistance. The conversation highlights the collaborative effort in correcting and improving understanding of quantum mechanics concepts.

Jun 4, 2022

warhammer

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.

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Jun 4, 2022

kuruman

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Last line ##4^2=16##. Other than that it looks good.

Jun 4, 2022

warhammer

kuruman said:

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

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