# intrep.m

Interaction representation transformation with respect to a specified Hamiltonian to specified order in perturbation theory (https://doi.org/10.1063/1.4928978).

## Syntax

   Hr=intrep(spin_system,H0,H,T,order)


## Arguments

   H0     - the Hamiltonian with respect to which the
interaction representation transformation
is to be done, typically Zeeman Hamiltonian

H      - laboratory frame Hamiltonian H0+H1 that is
to be transformed into the interaction rep-
resentation, typically the full Hamiltonian

T      - period of the H0 propagator

order  - perturbation theory order in the rotating
frame transformation, this may be inf


## Outputs

   Hr     - Hamiltonian in the interaction representation


## Examples

See 14N quadrupolar NMR examples (examples/nmr_solids/rframe_nqi_*.m) where the quadrupolar shift is a second order perturbation theory property.

## Notes

This module is called by context functions when the user specifies a numerical rotating frame transformation. It is generally a good idea to do this when your interactions are not much smaller than the Zeeman Hamiltonian, but you are not willing to run the calculation in the laboratory frame.