Abstract
In this work we are presenting a modified Coulomb potential function to describe the interaction between two micro-scopic electric charges. In particular, concerning the interaction between the proton and the electron in the hydrogen atom. The modified potential function is the product of the classical Coulomb potential and an oscillatory function dependent on a quantized phase factor. The oscillatory function picks up only selected points along the Coulomb potential, creating potential wells and barriers around the nucleus of the atom. The new potential reveals us new features of the hydrogen atom. Searching for a manner to determine the phase factor, we are using the concept of the de Broglie particle wavelike behavior and the quantum analogue of the virial theorem for describing the bound motion of a particle in a central force field. This procedure is a kind of feedback action, where we are making use of well established concepts of the quantum mechanics aiming to determine the phase factor of the new interaction potential.
Highlights
This work is the first of a series of four papers, for which we are revisiting, reexamining and questioning some points about the foundations of the atomic theory developed, mostly between the years 1910-1930, by many distinguished physicists: Niels Bohr, Erwin Schroedinger, Werner Heisenberg, Alberl Einstein, Max Born, Louis de Broglie and many others
How can the electron possibly know that certain positions around the nucleus of the atom are more likely to be occupied than others? [1] What is the real cause for this behavior for the electron? It is difficult to imagine the electron making regular probabilistic choice to occupy certain particular positions in the vicinity of the nucleus of the atom, based solely in the characteristics presented by the Coulomb potential
We can summarize this work as follows: For the hydrogen atom, the oscillatory potential function is able to predict correctly the values of the total energy and position of the electron in the atom, without the necessity of solving the time-independent Schroedinger wave equation. It shows several peculiarities of the hydrogen atom, such as: The existence of quantum wells and barriers, forming closed shells around nucleus of the atom. These wells constitute the most probable positions for the electron to occupy when moving around the nucleus of the atom; The emission or absorption of energy by the atom happens when the electron moves from one state of equilibrium to another by tunneling through these potential barriers created by the oscillatory potential; The new potential shows that the electric force between the proton and the electron oscillates, presenting negatives and positives peaks, the positive peaks represent regions where the interaction force between the proton and the electron is repulsive and the negative peaks where it is attractive, that is, the electron is always been pushed to the equilibrium position, which is a necessary condition for the stability of the atom
Summary
This work is the first of a series of four papers, for which we are revisiting, reexamining and questioning some points about the foundations of the atomic theory developed, mostly between the years 1910-1930, by many distinguished physicists: Niels Bohr, Erwin Schroedinger, Werner Heisenberg, Alberl Einstein, Max Born, Louis de Broglie and many others. What motivate us to produce this work are, in our opinion, some unclear and questionable points, that we believe still exist, concerning the applicability of the classical Coulomb potential for describing the interaction between two microscopic electric particles. What we want to say is that, the classical Coulomb potential reveal us only the macro-behavior of the interaction between electric particles This make us to suspect the existence of a different interaction potential, capable of describing more accurately the physics of the atoms, and be able to answer the questions formulated above. We believe that the choice of any potential function that proposes to be candidate to describe the interaction between two microscopic charges, in some way, needs to carry by itself the seeds of the quantum physics of the atom, that is, the quantization of the angular momentum and energy, both concepts, intimately related to the Heisenberg uncertainty principle. In some way, the new potential must be responsible to the wavelike nature of the particles
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