1. Simple man theory of Trojan wave packets (Larmor resonance in Hydrogen in electric field)

2. We all know Bohr result for quantisation of Hydrogen Energies are En=-1/n^2 and states with different l and m are degenerate

3. External electric field changes energy levels of Hydrogen (Stark effect) H=p^2/2m-1/r+e E

4. … so the magnetic field (Zeeman effect) H=p^2/2m-1/r+w L_z

5. True strong magnetic field adds harmonic oscillator so would be great if it was simpler… H=p^2/2m-1/r+(w_c/2) L_z +w_c^2/8(x^2+y^2)

6. It can be generated by the rotation H=U^+HU U=e^iwL_zt

7. Now we consider Hydrogen spectrum in simplified magnetic field It clearly changes … For hydrogen alone states with different l and m have the same energy for the same n For hydrogen in simplified magnetic field states with the same DIFFERENCES N-l and l-m have if only W=1/n^3 !!! (almost)

8. This how two spectra look

9. Now add electric field and new Stark states can be found Apply perturbation calculus for new degeracy (diagonalize perturbation matrix in bases of denerate states (almost)

10. And you get the result: One Stark state is perfectly Gaussian (Trojan wavepacket) (You can actualy diagonalize the infinite matrix from Perturbation Theory with degeneracy noticing that it is almost tridiagonal and pendular

11. But of course the simplified field does not exist so the packet must move with w in CP field and you get my result (Actualy the only known nondispersing wavepacket in linear quantum mechanics - they always spread in atoms)

12. But we also know that Stark eigenstates really do not exist (they are rather resonances since Stark perturbation series is usually divergent for real energy) So adding true magnetic field helps a bit (they now don’t ionize at all)