In a reasonably self-contained and explicit presentation we illustrate the efficiency of the Feynman–Kac formula for the rigorous derivation of three inequalities of interest in non-relativistic quantum mechanics.

Non-relativistic quantum mechanics for a free particle is shown to emerge from classical mechanics through the requirement of an invariance principle under transformations that preserve the Heisenberg position-momentum inequality. These transformations acting on the position and momentum uncertainties are induced by isotropic space dilatations. This invariance imposes a change in the laws of cl...

Motivated by relativity, several authors have suggested introducing, in classical and quantum physics, a separate time coordinate for every particle in order to avoid the use of simultaneity surfaces, e.g. [1–8]. For example, multi-time wave functions have been used in the foundations of quantum mechanics for defining relativistic collapse [9] or de Broglie–Bohm [10] theories. In quantum physic...

Motivated by relativity, several authors have suggested introducing, in classical and quantum physics, a separate time coordinate for every particle in order to avoid the use of simultaneity surfaces, e.g. [1–8]. For example, multi-time wave functions have been used in the foundations of quantum mechanics for defining relativistic collapse [9] or de Broglie–Bohm [10] theories. In quantum physic...

Motivated by relativity, several authors have suggested introducing, in classical and quantum physics, a separate time coordinate for every particle in order to avoid the use of simultaneity surfaces, e.g. [1–8]. For example, multi-time wave functions have been used in the foundations of quantum mechanics for defining relativistic collapse [9] or de Broglie–Bohm [10] theories. In quantum physic...

Bohmian trajectories have been used for various purposes, including the numerical simulation of the time-dependent Schrödinger equation and the visualization of time-dependent wave functions. We review the purpose they were invented for: to serve as the foundation of quantum mechanics, i.e., to explain quantum mechanics in terms of a theory that is free of paradoxes and allows an understanding ...

The pion form factor calculation in the " point-form " of relativistic quantum mechanics is reconsidered. Particular attention is given to the relation between the momentum of the system and the momentum transfer as well as to the quark current.

The electromagnetic current operator of a composite system must be a relativistic vector operator satisfying current conservation, cluster separability and the condition that interactions between the constituents do not renormalize the total electric charge. Assuming that these interactions are described in the framework of relativistic quantum mechanics of systems with a fixed number of partic...

We re-examine the justification for the imposition of regular boundary conditions on the wavefunction at the Coulomb singularity in the treatment of the hydrogen atom in non-relativistic quantum mechanics. We show that the issue of the correct boundary conditions is not independent of the physical structure of the proton. Under the physically reasonable assumption that the finite size and struc...

Let N(Z) denote the number of electrons which a nucleus of charge Z can bind in non-relativistic quantum mechanics (assuming that electrons are fermions). We prove that JV(Z)/Z-> 1 as Z-> oo.