Quantum relaxation in hydrogen eigenstates and two-state transitions

C. Colijn

C. Colijn, Edward R. Vrscay

The evolution of probability distributions for quantum systems defined by the de Broglie–Bohm causal interpretation of quantum mechanics is examined in the context of whether, in general, a non-|ψ|2 distribution will evolve to approximate a |ψ|2 distribution, as has been suggested by Bohm and others. This study focusses on hydrogen eigenstates and two-state hydrogen transitions stimulated by semi-classical radiation. It is shown that this process of ‘relaxation’ will not in general occur in such hydrogen systems, and thus that the de Broglie–Bohm theory must retain the |ψ|2 postulate if it is to be consistent with the standard quantum theory of individual systems.

L. K. Aminov

A.S. Davydov

Caroline Colijn

The de Broglie-Bohm causal interpretation of quantum mechanics is discussed, and applied to the hydrogen atom in several contexts. Prominent critiques of the causal program are noted and responses are given; it is argued that the de Broglie-Bohm theory is of notable interest to physics. Using the causal theory, electron trajectories are found for the conventional Schrödinger, Pauli and Dirac hydrogen eigenstates. In the Schrödinger case, an additional term is used to account for the spin; this term was not present in the original formulation of the theory but is necessary for the theory to be embedded in a relativistic formulation. In the Schrödinger, Pauli and Dirac cases, the eigenstate trajectories are shown to be circular, with electron motion revolving around the z-axis. Electron trajectories are also found for the 1s-2p0 transition problem under the Schrödinger equation; it is shown that the transition can be characterized by a comparison of the trajectory to the relevant eigenstate trajectories. The structures of the computed trajectories are relevant to the question of the possible evolution of a quantum distribution towards the standard quantum distribution (quantum equilibrium); this process is known as quantum relaxation. The transition problem is generalized to include all possible transitions in hydrogen stimulated by semi-classical radiation, and all of the trajectories found are examined in light of their implications for the evolution of the distribution to the standard distribution. Several promising avenues for future research are discussed.

Takahiro Yamaguchi

Stimulated Raman adiabatic passage method (STIRAP) is well known to be a very effective method for the efficient and selective transition between two molecular eigenstates in molecule. In this study, we generalize the STIRAP to be able to treat the transition to the non‐stationary state in the hydrogen bonded model system.