> 4) I have calculated the energy DOS for a lead and this looks correct, what I’m more
> unsure of is this the same as the DOS of the propagating modes. And I see how to find
> the velocity and things from the documentation, but is there a way to find the energy.
> Sorry if this is a stupid question I could not find anything on the forum

Not sure what you mean by this; the energy is an _input_ for calculating the DOS,

although by default a value of 0 is used (see the docs).

> 5) similar to question 1) how do I find things like the number of propagating modes.

`InfiniteSystem`s have a method called `modes` that will calculate you this:

    http://kwant-project.org/doc/1.0/reference/generated/kwant.system.InfiniteSystem#kwant.system.InfiniteSystem.modes

> 6) what is the best way to go about writing observables, sorry this is quite a general
> question and most likely up to the user, but for instance the pauli matrices are quite
> simple.

Yeah so support for this in kind of weak in Kwant at the moment. It will, unfortunately
probably be a case of creating the operator matrix yourself. We want to add support

or easily defining generic charge/current operators (e.g. spin along some magnetization

axis that changes through the system), but this is more do do with dealing with

multiple "orbitals" than things like the position operator.

> However the position operator, or velocity operator changes with the way the
> Hamiltonian is described, is there something simple general method to calculate these?

This will obviously depend on your model; Kwant doesn't know anything about

what basis your Hamiltonian is written in. In the general case you would need to
calculate the matrix elements of the observable in your chosen basis. For specific

cases this may not be as daunting as it sounds. e.g. for a continuum Hamiltonian

discretised on a  lattice the position operator is diagonal and each entry

is just the position of the corresponding site.