A note on the adiabatic theorem without gap condition

S. Teufel

Lett. Math. Phys. 58 (2001), 261-266.
[AWOGmp.ps (121.4 kB)]

Zusammenfassung

We simplify the proof of the adiabatic theorem of quantum mechanics without gap condition of Avron and Elgart [1] by providing an elementary solution of the "commutator equation". In addition, a minor modification of their argument allows for a more direct treatment of eigenvalue crossings. We also obtain simple, explicit conditions that yield information on the rate of convergence in the adiabatic limit.