- #1
dingo_d
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Homework Statement
I'm solving the quantum harmonic oscillator. And I'm solving Schrodinger equation. So I came up to one part where I have to use power series method of solving DE (that or Frobenius would probably work just fine). Now I have the recurrence relation:
[tex]a_{n+2}=\frac{\lambda(2n+1)-k^2}{(n+2)(n+1)}a_n[/tex]
And the text in which this is solved says that for [tex]n\ton\infty[/tex] that leads to asymptotic law
[tex]a_{n+2}=\frac{2\lambda}{n}a_n[/tex] corresponding to the series expansion of [tex]e^{\lambda x^2}[/tex].
Now, I tried looking at the limit, via L'Hospitals rule and I really can't see how they got that! :\
So can someone explain to me how they got that? Thanks...