A quantum Kolmogorov-Arnol'd-Moser-like theorem is formulated with use of an existence condition of a unique transformation between eigenstates of integrable and nonintegrable Hamiltonians. This condition determines the ability to assign local quantum numbers to eigenstates of nonintegrable Hamiltonians and explains localization phenomena.

• Received 13 May 1983

DOI:https://doi.org/10.1103/PhysRevLett.51.947