Uncertainty Principle and Stability of Atoms and Molecules

Stephen J. Gustafson, Israel Michael Sigal

Sir Harrie Massey

Yatendra Pal Varshni

Guy Ashkenazi, Ronnie Kosloff

A conceptually correct model for covalent bonding, suitable for teaching at the undergraduate general chemistry level, is presented. The quantum mechanical basis for the stability of the covalent bond can be derived from a qualitative discussion of the uncertainty principle, which relates the electron’s spatial confinement to its kinetic energy. The qualitative discussion is backed by quantitative data obtained from the analytical quantum mechanical solution of the H2+ molecule. In addition, the stability of molecules is used as a tangible background against which the inferences emerging from the philosophical debate between classical determinism and the Copenhagen interpretation can be tested.

Anurag Chapagain

Abstract: It is a well-known fact in physics that classical mechanics describes the macro-world, and quantum mechanics describes the atomic and sub-atomic world. However, principles of quantum mechanics, such as Heisenberg’s Uncertainty Principle, can create visible real-life effects. One of the most commonly known of those effects is the stability problem, whereby a one-dimensional point base object in a gravity environment cannot remain stable beyond a time frame. This paper expands the stability question from 1- dimensional rod to 2-dimensional highly symmetrical structures, such as an even-sided polygon. Using principles of classical mechanics, and Heisenberg’s uncertainty principle, a stability equation is derived. The stability problem is discussed both quantitatively as well as qualitatively. Using the graphical analysis of the result, the relation between stability time and the number of sides of polygon is determined. In an environment with gravity forces only existing, it is determined that stability increases with the number of sides of a polygon. Using the equation to find results for circles, it was found that a circle has the highest degree of stability. These results and the numerical calculation can be utilized for architectural purposes and high-precision experiments. The result is also helpful for minimizing the perception that quantum mechanical effects have no visible effects other than in the atomic, and subatomic world. Keywords: Quantum mechanics, Heisenberg Uncertainty principle, degree of stability, polygon, the highest degree of stability

Thomas A. Brody