This is a 2 part question:

1). I am looking for a (hopefully accessible to beginning grad student who knows matrix perturbation theory) reference for doing concrete calculations of perturbed discrete spectra for operators that also have continuous spectrum. We can assume perturbation is compact and hence continuous spectrum is unchanged. What would be your recommendations ? Are there any toolboxes that already exist to do such computations ?

2). As I understand, the main issue is that now one has to project onto the subspace corresponding to continuous spectra.

However, in computations, continuous spectra is approximated by additional discrete spectra. Can I expect to find reliable answers if I just a very high resolution and apply the algorithms used for purely discrete case to the resulting data ?

This is a 2 part question:

1). I am looking for a (hopefully accessible to beginning grad student who knows matrix perturbation theory) reference for doing concrete calculations of perturbed discrete spectra for operators that also have continuous spectrum. We can assume perturbation is compact and hence continuous spectrum is unchanged. What would be your recommendations ? Are there any toolboxes that already exist to do such computations ?

2). As I understand, the main issue is that now one has to project onto the subspace corresponding to continuous spectra.

However, in computations, continuous spectra is approximated by additional discrete spectra. Can I expect to find reliable answers if I just a very high resolution and apply the algorithms used for purely discrete case to the resulting data ?

Is there any tutorial available anywhere ? I assume physicists are doing these types of calculations all the time, so something digestible must be out there ?

This is a 2 part question:

1). I am looking for a (hopefully accessible to beginning grad student who knows matrix perturbation theory) reference for doing concrete calculations of perturbed discrete spectra for operators that also have continuous spectrum. What would be your recommendations ? Are there any toolboxes that already exist to do such computations ?

2). As I understand, the main issue is that now one has to project onto the subspace corresponding to continuous spectra.

However, in computations, continuous spectra is approximated by additional discrete spectra. Can I expect to find reliable answers if I just a very high resolution and apply the algorithms used for purely discrete case to the resulting data ?

This is a 2 part question:

1). I am looking for a (hopefully accessible to beginning grad student who knows matrix perturbation theory) reference for doing concrete calculations of perturbed discrete spectra for operators that also have continuous spectrum. We can assume perturbation is compact and hence continuous spectrum is unchanged. What would be your recommendations ? Are there any toolboxes that already exist to do such computations ?

2). As I understand, the main issue is that now one has to project onto the subspace corresponding to continuous spectra.

However, in computations, continuous spectra is approximated by additional discrete spectra. Can I expect to find reliable answers if I just a very high resolution and apply the algorithms used for purely discrete case to the resulting data ?