Recent content by Arya_

Hi All, Greetings! I have a 3d material and I use result from first principal for getting the potential (U(x,y,z)). I then find average U(x) from U(x,y,z). Now if I write one dimensional Hamiltonian in X direction and use this value of U(x), can I get bandgap of the original 3d material (I...

Hi All, Greetings ! Here is what I wish to know. Specifying a tight binding hamiltonian requires values of potential (U). Consider a 3d solid. If I have potential profile in x direction (U1, U2, U3...so on) can I directly plug in these U values into the tight binding hamiltonian or do I...

Hi All, I was going through a paper on quantum simulations. Below is an extract from the paper; I would be obliged if anyone can help me to understand it: We will use eigenstate representation for transverse direction(HT) and real space for longitudinal direction(HL) Hamiltonians. HL=...

Well now I am confused. Referring to my last reply, how would you interpret the eigenvalues obtained from [d,v] = eig(H). Is that only for a particular K? However in setting up H in my original post we did not even talked about K . All that was considered is a potential U.

Now, given a matrix H , [d,v] = eig(H) in MATLAB gives me d = diagonal eigenvalue matrix and v = matrix columns of which are eigenstates. This would mean each diagonal element in d is eigenvalue of corresponding column in v. Thus I have a set of eigenstates and corresponding eigenvalues. Where...

Does that mean if I look at Eigenvalues of H and find gaps in energy numbers those are bandgaps. In short can I find bandgap by looking at eigenvalues?

Hi All, My question is more from applied quantum mechanics. Suppose I have a 2D conductor(or semiconductor). I use eigenstate representation of hamiltonian in transverse direction and real space representation in longitudinal direction (direction of current flow). Now, 1. Hω=Eω , ω being...