(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

For the Harmonic Oscillator, the state |ψ> = (|0> + |1>) / √(2)

Find [itex]\overline{x}[/itex] = <ψ|x|ψ> [itex]\overline{p}[/itex] = <ψ|p|ψ>

[itex]\overline{x^2}[/itex] = <ψ|x[itex]^{2}[/itex]|ψ> and [itex]\overline{p^2}[/itex] = <ψ|p[itex]^{2}[/itex]|ψ>

and

<ψ| (x - [itex]\overline{x}[/itex])^2 |ψ><ψ| (p - [itex]\overline{p}[/itex])^2 |ψ>

2. Relevant equations

3. The attempt at a solution

I got some help from another student on getting started with the first part of this problem, but in all honesty I'm really not even sure how to start some of these, and how the operators work. This is what I've got so far:

<ψ|x|ψ> = <ψ|√(hbar/2mω) (a+a_)|ψ>

<ψ| = 1/√2 (<0| + <1|)

|ψ> = 1/√2 (|0> + |1>)

giving 1/2 √(hbar/2mω) (<0| + <1|) (a+a_) (|0> + |1>)

from here the raising and lowering operators are operating on the nth states of 0 and 1. I know that a_|0> = 0 and a_|n> = √(n)|n-1> and that a+|n> = √(n+1)|n+1> but if anyone can make a suggestion or show me how to get some results here, I would greatly appreciate it. As well, some direction on how to start the next parts would be amazing too, thank you!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Expectation values and the Harmonic oscillator

**Physics Forums | Science Articles, Homework Help, Discussion**