73 citations · 307 across the 13 of their papers we have counts for
14 papers · 1 filter
Generating Function and a Rodrigues Formula for the Polynomials in -Dimensional Semiclassical Wave Packets
George A. Hagedorn
We present a simple formula for the generating function for the polynomials in the --dimensional semiclassical wave packets. We then use this formula to prove the associated Rod…
Explicit Bound States for Certain N-Body Hamiltonians
George A. Hagedorn, Edward F. Valeev
We construct explicit bound state wave functions and bound state energies for certain --body Hamiltonians in one dimension that are analogous to --electron Hamiltonians for (…
A note on the switching adiabatic theorem
Alexander Elgart, George A. Hagedorn
We derive a nearly optimal upper bound on the running time in the adiabatic theorem for a switching family of Hamiltonians. We assume the switching Hamiltonian is in the Gevrey cla…
Exponentially Accurate Semiclassical Tunneling Wave Functions in One Dimension
Vasile Gradinaru, George A. Hagedorn, Alain Joye
We study the time behavior of wave functions involved in tunneling through a smooth potential barrier in one dimension in the semiclassical limit. We determine the leading order co…
An Adiabatic Theorem for Resonances
Alexander Elgart, George Hagedorn
We prove a robust extension of the quantum adiabatic theorem. The theorem applies to systems that have resonances instead of bound states, and to systems for which just an approxim…
A Mathematical Theory for Vibrational Levels Associated with Hydrogen Bonds II: The Non--Symmetric Case
George A. Hagedorn, Alain Joye
We propose an alternative to the usual time--independent Born--Oppenheimer approximation that is specifically designed to describe molecules with non--symmetrical hydrogen bonds. I…