Non-relativistic quantum mechanics is necessarily an approximation to relativistic quantum mechanics. It is valid in the regime where kinetic energies and potential energies (more generally field energies) are much less than the rest mass energies of particles. Following philosophy of Laughlin (2005), I prefer to think of non-relativistic quantum mechanics as an emergent theory: one that is exa...

We reformulate the ‘separated quantum entities’ theorem, i.e. the theorem that proves that two separated quantum entities cannot be described by means of standard quantum mechanics, within the fully elaborated operational Geneva-Brussels approach to quantum axiomatics, where the basic mathematical structure is that of a State Property System. We give arguments that show that the core of this re...

Based on a general formulation for discrete-time quantum mechanics, introduced in 1], symmetries in discrete-time quantum mechanics are investigated. It is shown that any classical continuous symmetry leads to a conserved quantity in classical mechanics, as well as quantum mechanics. The transformed wave function, however, has the correct evolution if and only if the symmetry is nonanomalous.

In this paper we study properties of symbols such that these belong to class of symbols sitting insideSm ρ,φ that we shall introduce as the following. So for because hypoelliptic pseudodifferential operatorsplays a key role in quantum mechanics we will investigate some properties of M−hypoelliptic pseudodifferential operators for which define base on this class of symbols. Also we consider maxi...

The uncertainty principle is one of the fundamental principles of quantum mechanics . While studying quantum mechanics recently, the author made an exciting mathematical discovery about the product of two expectation values. The author explains the discovery. Sec. I . Introduction In quantum mechanics there is no such concept as the path of a particle. This forms the content of what is called t...

Bohmian mechanics is an alternative interpretation of quantum mechanics. We outline the main characteristics of its non-relativistic formulation. Most notably it does provide a simple solution to the infamous measurement problem of quantum mechanics. Presumably the most common objection against Bohmian mechanics is based on its non-locality and its apparent con ict with relativity and quantum e...