Sources of Quantum Mechanics

W. M. Stuckey, Timothy J. McDevitt, Michael Silberstein

We propose a discrete path integral formalism over graphs fundamental to quantum mechanics (QM) based on our interpretation of QM called Relational Blockworld (RBW). In our approach, the transition amplitude is not viewed as a sum over all field configurations, but is a mathematical machine for measuring the symmetry of the discrete differential operator and source vector of the discrete action. Therefore, we restrict the path integral to the row space of the discrete differential operator, which also contains the discrete source vector, in order to avoid singularities. In this fashion we obtain the two-source transition amplitude over a "ladder" graph with N vertices. We interpret this solution in the context of the twin-slit experiment.

Mark S. Hillery

A null test of quantum mechanics is proposed. It is based on an arrangement in which a source sends two signals to two detectors. At each detector one of two different quantities can be measured. If the source satisfies three conditions, all of which can be verified experimentally, then, according to quantum mechanics, a particular outcome is forbidden. This result follows only from the way in which quantum mechanics constructs probabilities, and does not involve any dynamics. Looking for this outcome is a test of quantum mechanics. It is shown how this test can be realized using two-photon down-conversion.

David Favrholdt

Caio Lima Firme

Main features:i) A different approach for teaching Quantum Mechanics encompassing old quantum mechanics, matrix mechanics and wave mechanics in a historical perspective which helps to consolidate most important concepts of Quantum Mechanics;ii) Original information from the most important papers of Quantum Mechanics;iii) Derivation of all important equations of Quantum Mechanics, for example, Heisenberg’s uncertainty principle, de Broglie’s wave-particle duality, Schrödinger’s wave equation, etc., showing their interrelations through Dirac’s equations and other applications of matrix and wave mechanics;iv) Comprehensive mathematical support for the understanding of Quantum Mechanics; derivation of all equations make reading easier;v) The illustrations of the book cover examples, exercises and do-it-yourself activities;vi) Fundamentals of Fortran and numerical calculation along with the source codes for numerical solutions of several mathematical and quantum problems. All source codes are in the author’s site: (https://www.fortrancodes.com/);vii) Chapters devoted to linear algebra and differential equations applied to quantum mechanics and their numerical solutions;viii) Complete solution for the one-electron and two-electron problems using Schrödinger’s time independent equation along with their source codes.