Symplectic propagator

[JanosJiri]

I'm not 100 % sure this propagator with the field is time-reversible. Maybe I should use the ideas from Ulrich's book.

subroutine propag_rt_1d()

  ! Propagating with H matrix: half step
  call propag_H_rt_1d(.true.)

  ! Propagating istate with T matrix: full step
  call propag_T_rt_1d()

  ! Propagating with H matrix: half step
  call propag_H_rt_1d(.false.)

end subroutine propag_rt_1d```

It would also be simple to use half-step in kinetic energy and then do a step in potential energy, where the Hamiltonian would be evaluated in the middle. This would make it symplectic/time-reversible and at the same time I would reduce matrix diagonalization operations.

[JanosJiri]

It would also be simple to use half-step in kinetic energy and then do a step in potential energy, where the Hamiltonian would be evaluated in the middle. This would make it symplectic/time-reversible and at the same time I would reduce matrix diagonalization operations.

[JanosJiri]

Other option is to use the laser pulse in the t + dt/2