Dear Kwant users,
Solving Schrodinger equantions describing quantum physics of noninteracting systems amounts to solving eigenproblems. As I know, the Kwant package has the superiority at calculating transport properties, and moreover, it can also solve eigenproblems of closed systems. To be precise, firstly, one can use "kwant.continuum.discretize" to discrete continous Hamiltonians into tight-binding models with a specified lattice constant, and secondly, diagonalize the lattice model to obtain the eigen-energies and eigen-wavefunctions. Actually, we can solve Schrodinger equantions, which are essentially second-order partial differential equations, by numerical methods such as the powerful finite-element-method with irregular mesh and specified boudary conditions. I know that many papers in codensed matter community studying finite-size models by the tight-binding method rather than the finite-element-method. Is this due to any restriction of the finite-element-method in solving Schrodinger equantion? Does anyone ever compare the performance of tight-binding-method and finite-element-method on solving eigenproblem of closed Hamiltonian. Is there any literature addressing this issue? Regards, Zhan
