On the Adiabatic Theorem in Quantum Theory

On the Adiabatic Theorem in Quantum Theory Synopsis

Whilst the greatest effort has been made to ensure the quality of this text, due to the historical nature of this content, in some rare cases there may be minor issues with legibility. In order to determine the leading term of the asymptotic expansion of the solution T we can no longer rely on standard methods. A close analysis shows that the degeneracy corres ponds exactly to the occurrence of a turning point in the terminology of the asymptotic theory of ordinary differential equations. The turning point encountered here is of a type which.is somewhat different thanishat customarily treated; in fact, it is of a somewhat simpler type. It is not diffi cult to obtain the formulas for the transition across such a turning point.