MOLECULAR PROPAGATION THROUGH SMALL AVOIDED CROSSINGS OF ELECTRON ENERGY LEVELS

This is the second of two papers on the propagation of molecular wave packets through avoided crossings of electronic energy levels in a limit where the gap between the levels shrinks as the nuclear masses are increased. An earlier paper deals with the simplest two types of generic, minimal multiplicity avoided crossings, in which the levels essentially depend on only one of the nuclear configuration parameters. The present paper deals with propagation through the remaining four types of generic, minimal multiplicity avoided crossings, in which the levels depend on more than one nuclear configuration parameter.

[1]  Vimal Singh,et al.  Perturbation methods , 1991 .

[2]  Alexander Elgart,et al.  The Adiabatic Theorem of Quantum Mechanics , 1998 .

[3]  G. Hagedorn.  Classification and normal forms for avoided crossings of quantum-mechanical energy levels , 1998 .

[4]  J. S. Howland,et al.  THE BORN OPPENHEIMER APPROXIMATION: STRAIGHT-UP AND WITH A TWIST , 1997 .

[5]  A. Joye.  Exponential asymptotics in a singular limit for n -level scattering systems , 1995, quant-ph/9508013.

[6]  C. Pfister,et al.  Semiclassical asymptotics beyond all orders for simple scattering systems , 1995 .

[7]  G. Nenciu,et al.  Semi-Classical Inelastic S-Matrix for One-Dimensional N-States Systems , 1995 .

[8]  A. Kargol.  The infinite time limit for the time-dependent Born-Oppenheimer approximation , 1994 .

[9]  Alain Joye,et al.  Non-trivial prefactors in adiabatic transition probabilities induced by high-order complex degeneracies , 1993 .

[10]  Pfister,et al.  Non-Abelian geometric effect in quantum adiabatic transitions. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[11]  C. Pfister,et al.  Superadiabatic evolution and adiabatic transition probability between two nondegenerate levels isolated in the spectrum , 1993 .

[12]  M. Klein,et al.  On the Born-Oppenheimer approximation of wave operators in molecular scattering theory , 1993 .

[13]  C. Pfister,et al.  Absence of geometrical correction to the Landau-Zener formula , 1992 .

[14]  Mileti,et al.  Interferences in adiabatic transition probabilities mediated by Stokes lines. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[15]  Alain Joye,et al.  Exponential decay and geometric aspect of transition probabilities in the adiabatic limit , 1991 .

[16]  André Martinez.  Resonances dans l'approximation de Born-Oppenheimer II-largeur des resonances , 1991 .

[17]  G. Hagedorn.  Proof of the Landau-Zener formula in an adiabatic limit with small eigenvalue gaps , 1991 .

[18]  C. Pfister,et al.  Full asymptotic expansion of transition probabilities in the adiabatic limit , 1991 .

[19]  George A. Hagedorn,et al.  Electron energy level crossings in the time-dependent Born-Oppenheimer approximation , 1990 .

[20]  G. Hagedorn.  High order corrections to the time-dependent Born-Oppenheimer approximation. II: Coulomb systems , 1988 .

[21]  G. Hagedorn.  High order corrections to the time-independent Born-Oppenheimer approximation II: Diatomic Coulomb systems , 1988 .

[22]  M. Klein.  On the mathematical theory of predissociation , 1987 .

[23]  George A. Hagedorn,et al.  "High Order Corrections to the Time-Dependent Born-Oppenheimer Approximation I: Smooth Potentials" , 1986 .

[24]  J. Cole,et al.  Perturbation Methods in Applied Mathematics , 1969 .

[25]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[26]  Tosio Kato.  On the Adiabatic Theorem of Quantum Mechanics , 1950 .

[27]  George A. Hagedorn,et al.  Landau-Zener transitions through small electronic eigenvalue gaps in the Born-Oppenheimer approximation , 1998 .

[28]  George A. Hagedorn,et al.  Molecular propagation through electron energy level crossings , 1994 .

[29]  A. Joye.  Proof of the Landau–Zener formula , 1994 .

[30]  C. Pfister,et al.  Quantum adiabatic evolution , 1994 .

[31]  Ruedi Seiler,et al.  On the Born-Oppenheimer expansion for polyatomic molecules , 1992 .

[32]  A. Martínez.  Développements asymptotiques et effet tunnel dans l'approximation de Born-Oppenheimer , 1989 .

[33]  André Martinez.  Développements asymptotiques dans l'approximation de Born-Oppenheimer@@@Asymptotic expansions in the Born-Oppenheimer approximation , 1988 .

[34]  G. Hagedorn.  Semiclassical quantum mechanics, IV : large order asymptotics and more general states in more than one dimension , 1985 .

[35]  M. Reed.  Methods of Modern Mathematical Physics. I: Functional Analysis , 1972 .