- #1
gronke
- 2
- 0
Homework Statement
Homework Equations
The Attempt at a Solution
I solved part a) correctly, I believe, giving me
ψ = e[itex]^{-(√(km)/\hbar)x^{2}}[/itex]
and a normalization constant A = ((π[itex]\hbar[/itex])/(km))[itex]^{-1/4}[/itex]
I'm having difficulty with part b. I'm not exactly sure how I create a linear combination. I think I'm supposed to write the linear combination like so:
a + a[itex]^{+}[/itex] = 2(k/2)[itex]^{1/2}[/itex]x
(a + a[itex]^{+}[/itex])(2k[itex]^{-1/2}[/itex]) = x
However, I am not sure how I use the operator methods to show that xψ0 is the first excited state.
If anyone could nudge me in the right direction, I'd be eternally grateful! Thank you.