- #1
JamesJames
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Consider a particle in a harmonic pscillator potential V (x) is given by
[tex]V = \frac{1}{2}m\omega^2[/tex]
Also [tex]\hat a = n^\frac{1}{2}|n-1>[/tex], and
[tex]\hat a\dagger = (n-1)^\frac{1}{2}|n-1>[/tex]
where
[tex]
\hat a = \frac{\beta}{\sqrt 2}(\hat x + \frac{i\hat p}{m\omega})
[/tex]
[tex]
\hat a\dagger = \frac{\beta}{\sqrt 2}(\hat x - \frac{i\hat p}{m\omega})
[/tex]
Construct a matrix representation for
[tex]\hat a[/tex]
[tex]\hat a\dagger[/tex]
[tex]\hat N = \hat a\hat \dagger[/tex]
and
[tex]\hat H[/tex]
where[tex]\hat H[/tex] is the Hamiltonian.
If someone can show me one and explain it to me, I will try the rest by myself before asking questions about them.
I am really desparate
Please help
James
[tex]V = \frac{1}{2}m\omega^2[/tex]
Also [tex]\hat a = n^\frac{1}{2}|n-1>[/tex], and
[tex]\hat a\dagger = (n-1)^\frac{1}{2}|n-1>[/tex]
where
[tex]
\hat a = \frac{\beta}{\sqrt 2}(\hat x + \frac{i\hat p}{m\omega})
[/tex]
[tex]
\hat a\dagger = \frac{\beta}{\sqrt 2}(\hat x - \frac{i\hat p}{m\omega})
[/tex]
Construct a matrix representation for
[tex]\hat a[/tex]
[tex]\hat a\dagger[/tex]
[tex]\hat N = \hat a\hat \dagger[/tex]
and
[tex]\hat H[/tex]
where[tex]\hat H[/tex] is the Hamiltonian.
If someone can show me one and explain it to me, I will try the rest by myself before asking questions about them.
I am really desparate
Please help
James
Last edited: