There has been spectacular progress in laser technology in recent years, so that it is now possible to make laser pulses which are much shorter than the characteristic time scale for chemical bond for mation and breaking. These pulses can be shaped in time and frequency with great precision, and sequences of such pulses can be orchestrated.
In the last few years we have developed a method to solve both the time-independent and time-dependent Schrödinger equations based on the von Neumann (vN) lattice of phase space Gaussians. By incorporating periodic boundary conditions into the vN lattice we solve a longstanding problem of convergence of the vN method. This opens the door to tailoring quantum calculations to the underlying classical phase space structure while retaining the accuracy of the Fourier grid basis. Formally the method defeats exponential scaling with dimensionality. In the classical limit the method reaches the remarkable efficiency of 1 converged eigenstate per 1 basis functions. We have used the method to calculate the vibrational eigenstates of a polyatomic with 104 bound states and to simulate attosecond one-electron and two-electron dynamics in the presence of combined strong XUV and NIR laser fields. The method also has applications to signal and image processing.
Ever since the advent of Quantum Mechanics, there has been a quest for a trajectory based formulation of quantum theory that is exact. In the 1950’s, David Bohm developed an exact formulation of quantum mechanics in which trajectories evolve in the presence of the usual Newtonian force plus an additional quantum force. However, closer inspection of the Bohmian formulation reveals that the nonlocality of quantum mechanics has not disappeared --- it has simply been swept under the rug into the quantum force.
It is generally believed that all molecular processes are ultimately governed by the laws of quantum mechanics. This includes the central event in chemistry --- a chemical reaction --- in which reactants come together, exchange partners and separate into products. The quantum mechanical theory for chemical reactions is called "scattering theory", and it is the underlying theory behind all chemical transformations.
