Recent content by partyday

Hello, I am interested in the following model: $$ H = \sum_{<i,j>} -t (c_i c_j^{\dagger} + \text{H.C.}) + U (n_i n_j) + \sum_{<<i,j>>} -t' (c_i c_j^{\dagger} + \text{H.C.}) + U' (n_i n_j) $$ where \( <i,j> \) indicates nearest neighbors, and \( <<i,j>> \) indicates next-nearest neighbors...

I think I see the solution now. Bit of a brainfart for me. The ratios of the first and second derivative are the same for an odd or even function at x and -x, and that means that by that fact it's either ##\psi(x) = \psi(-x) ## (even) or ##\psi(x) = - \psi(-x)## (odd) right?

C is just the constant by ##\psi''## My initial attempt was to write out the Schrödinger equation in the case that x>0 and x<0, so that $$ \frac {\psi'' (x)} {\psi (x)} = C(E-V(x))$$ and $$ \frac {\psi'' (-x)} {\psi (-x)} = C(E-V(-x))$$ And since V(-x) = V(x) I equated them and...