Recent content by jtaa

ok i get a second order diff equation that looks like this: http://dl.dropbox.com/u/2399196/2orderdiff.png but how do i solve that?

here is a link to the pdf file with my question and answershttp://dl.dropbox.com/u/2399196/harmonic%20osc.pdf i'm not sure where to start, because i don't want to assume anything that i haven't been given. i'm stuck on part (iv) where i have to derive explicit expressions for 2 wave functions...

can i simply say after that: the energies are: En=hw(n+\frac{1}{2}) ?

Hϕ0=\frac{1}{2}ℏωϕ0 So, E0=\frac{1}{2}ℏω => Hϕn+1 = ℏωϕn+1+Enϕn+1 ?

it assumes that Hϕn = nϕn i.e. that ϕn is an eigenvector of H. n being the eigenvalue => = (\hbar\omega+n)ϕn+1 ?

i then get: =(n+1)-1/2(a†\hbar\omega+a†H)\phin =\hbar\omega\phin+1 + (n+1)-1/2a†H\phin not sure what to do from here..

re-order how? by using: Ha†=\hbar\omegaa† + a†H ?

[H,a†] = \hbar\omegaa† [H,a] = -\hbar\omegaa

N=a†a [N,a†]=a† [N,a]=-a

the problem is attached as an image. im having troubles with the question. I'm assuming this is an induction question? i can prove it for the basis step n=0. but I am having trouble as to what i have to do for n+1 (inductive step). any help or hints would be great!thanks