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...