Interacting Quantum Trajectories in Multidimensional Systems

Time propagation of non-relativistic spin-free quantum systems can be modeled with ensembles of real-valued interacting trajectories obeying a Newton-like equation. This approach is like the de Broglie-Bohm (dBB) theory in that the trajectories produced are identical, and it provides the same experimental predictions as the traditional formalism involving the time-dependent Schrödinger equation. Differing from the dBB theory, it does not have a pilot wave or wavefunction and the source of quantum effects comes from the interactions between trajectories. Commonly known as “Interacting Quantum Trajectories” (IQT), this method has captured the interest of those in both computational chemistry and physics communities due to not only new possible ontological insights, but also due to possible computational advantages. Eliminating the wavefunction may provide a way to avoid the exponential scaling in computation as one adds a new constituent to a quantum system, commonly known as the “curse of dimensionality”. So far, computational techniques have been developed to handle the IQT formalism in non-relativistic spinless and spin 1/2 systems both for the 1 DOF case. Although the many-DOF equations for IQT have been developed, computational techniques for these systems are still being explored. Strategies to handle the 2-DOF test case involving two identical particles obeying Bose-Einstein statistics, i.e., bosons, in a harmonic oscillator potential, will be presented.