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...

A force field for vanadium-oxos was developed and tested with a variety of complexes with coordination numbers of 5 or 6 and formal oxidations states of +4 or +5 on the metal. Similarly, a semiempirical quantum mechanical method for transition metals was extended to vanadium. In this research soft and hard ligands were studied, as were ligands coordinated through single, multiple, and dative bo...

In contrast to the Copenhagen interpretation we consider quantum mechanics as universally valid and query whether classical physics is really intuitive and plausible.-We discuss these problems within the quantum logic approach to quantum mechanics where the classical ontology is relaxed by reducing metaphysical hypotheses. On the basis of this weak ontology a formal logic of quantum physics can...

Mermin’s “shut up and calculate!” somehow summarizes the most widely accepted view on quantum mechanics. This conception has led to a rather constraining way to think and understand the quantum world. Nonetheless, a closer look at the principles and formal body of this theory shows that, beyond longstanding prejudices, there is still room enough for alternative tools. This is the case, for exam...