Recent content by GeneralGrant

I have to solve it numerically, I'm pretty sure of that. But i know know what the expression $$ < O | \hat{H} | O > $$ means other then it is an inner product of the matrix $\hat{H}$ and O and then a product with the transpose of O. I think its supposed to representable as an integral somehow...

Homework Statement Given the potential V(x) = - 1/ sqrt(1+x^2) Consider this in a 50x50 matrix representation of the hamiltonian in the basis of a one dimensional harmonic oscillator. Determine the eigenvalues and eigenvecotrs, the optimal parameter for the basis, and cop ate the...

I have done so for the harmonic oscillator, which is one way that i got my X and P for the HO. And have tried to use the X and P forms from the HO in my Hamiltonian in question, but because its 1/Sqrt(1+x^2) i always end up dividing by a zero for the none tri-diagonal terms.(using 1 = identity...

Hello readers, Given the potential V(x) = - 1/ sqrt(1+x^2) I have found numerically 12 negative energy solutions Now I want to try to solve for these using matrix mechanics I know the matrix form of the harmonic oscillator operators X_ho, P_ho. I believe I need to perform the...

Thanks guys for the responses, timely too. I was able to successfully plot all possible solutions, since this is my third attempt at writing a reply, i was not logged in and deleted my replays twice now, and i have work to do i will just say that from reading your responses i now understand...

Hello everybody/reader, Thank you for reading my post, i have been known to be long winded but i put a abridged version of my question and sectional labels so it can be skimmed easily for relevant information. note: I Wrote a very explanatory post, which had sections and was written...