The puzzling entanglement of Schrödinger's wave function

O. Giraud, Bertrand Georgeot, John Martin

Y. S. Huang, Yu Jia, Rui Yu

We revisit the coalescence behavior of the atomic Schr\"odinger wave functions from the angle of an operator-product expansion (OPE) within the nonrelativistic Coulomb-Schr\"odinger effective-field theory. We take the electron-nucleus coalescence as an explicit example to demonstrate our formalism, by proving an exact OPE relation to all orders in perturbation theory. As a consequence, the celebrated Kato's cusp condition can be readily reproduced. Our approach can be readily extended to ascertain the multiparticle coalescence behaviors of atomic wave functions, which are otherwise difficult to achieve from the conventional Schr\"odinger equation approach. Moreover, by incorporating relativistic effects, our OPE approach appears to be able to provide key insight for solving a 90-year-old puzzle concerning the peculiar coalescence behavior of the wave function for a Dirac hydrogen atom.

Moncy Vilavinal John

Some recent experiments claim to show that any model in which a quantum state represents mere information about an underlying physical reality of the system must make predictions which contradict those of quantum theory. The present work undertakes to investigate the issue of reality, treading a more fundamental route from the Hamilton-Jacobi equation of classical mechanics to the Schrodinger equation of quantum mechanics. Motivation for this is a similar approach from the eikonal equation in geometrical optics to the wave equation in electromagnetic theory. We rewrite the classical Hamilton-Jacobi equation as a wave equation and seek to generalise de Broglie's wave particle duality by demanding that both particle and light waves have the freedom of being described by any square-integrable function. This generalisation, which allows superposition also for matter wave functions, helps us to obtain the Schrodinger equation, whose solution can be seen to be as much objective as the classical mechanics wave function. Several other equations which one writes in quantum mechanics, including the eigenvalue equations for observables, series expansion of energy states in terms of eigenstates of observables other than energy, etc., can be written in the classical case too. Absence of any collapse of the wave function, entanglement, etc. in the classical realm have their origin in the nonlinearity of the classical wave equation. These considerations indicate that many of the puzzles in quantum mechanics are present also in classical mechanics in a dormant form, which fact shall help to demystify quantum mechanics to a great extent.

Jeffrey Bub

Chen, C. Y.

The textbook treatment in that the wave function of a dynamical system is expanded in an eigenfunction series is investigated. With help of an elementary example and some mathematical theorems, it is revealed that in terms of solving the time-dependent Schrödinger equation the treatment involves in divergence trouble . The root reason behind the trouble is finally analyzed.