Multivaluedness

Longuet-Higgins corrected the multivaluedness of the elechonic eigenfunctions by multiplying them with a phase factor, namely,... 

Appendix C On the Single/Multivaluedness of the Adiahatic-to-Diahatic Transformation Matrix Appendix D The Diabatic Representation Appendix E A Numerical Study of a Three-State Model Appendix F The Treatment of a Conical Intersection Removed from the Origin of Coordinates Acknowledgments References... 

One way to eliminate the multivaluedness of the electronic eigenfunctions is by multiplying it by a phase factor [15], namely. 

APPENDIX C ON THE SINGLE/MULTIVALUEDNESS OF THE ADIABATIC-TO-DIABATIC TRANSFORMATION MATRIX... 

The nature of the above distortion leads to an associated multivaluedness in the vibrational quantum number, which can be attributed to the fact that the twist angle of the classical invariant tori increases 2n on a cycle around the critical singularity. 

Unfortunately it is not always possible to use only linear inequalities. In further studies we will have to include into the kinetic constraints both the equations of nonlinear chemical kinetics and the nonlinear equations of transfer processes. Nonconvexity of the problem solved and possible multivaluedness of its solutions, in case the constraints on radiant heat exchange are included into MEIS, are shown in the work by Kaganovich et al. (2005a). 

When this is done, the reader can see that Laplace inversion is formally equivalent to contour integration in the complex plane. We shall see that exceptional behavior arises occasionally (singularities owing to multivaluedness, for example) and these special cases will be treated in the sections to follow. Our primary efforts will be directed toward the usual case, that is, pole and multiple pole singularities occurring in the Laplace transform function Fis). 

---