Quantum Mechanics

Quantum mechanics is mentally challenging because of two factors:

  1. The factor that makes it mysterious
  2. The factor that makes it mathematically difficult

However, the factor that makes it mysterious is not difficult, and the factor that makes it difficult is not mysterious.

The factor that makes quantum mechanics mysterious is that particles act as both particles and waves. That mystery vanishes, however, when one considers particles and their virtual photons. Virtual photons are the signals between particles that enable them to exert forces on other particles at a distance. The de Broglie equation that quantifies this wave nature of matter can be derived by assuming that the virtual photon is the particle mass’s energy equivalent, and that the particle converts back and forth from particle to virtual photon. The derivation is attached.

The difficult part of quantum mechanics is that once you have more than 2 mutually interacting particles, you have a classic 3 body problem when you try to find the paths of the particles. An exact solution to the 3 body problem has never been found in mathematics. So it is necessary to make approximations when trying to put together a 3 dimensional picture of 3 or more interacting particles, and putting that picture together (of electron densities around a nucleus) is difficult in the first place. There is nothing more mysterious about this aspect of quantum mechanics than in one electron atoms. It just involves esoteric mathematics.

 

 

De Broglie Derivation from Physical Model

Suppose that a particle is in equilibrium with its energy (or standing wave) form. That is, the particle exists part of the time as its own virtual photon, and the photon has the energy equivalent of the particle’s ,mass. The wavelength of the photon is:

 

 

so  

so = and  

Say this particle (and its virtual photon) pass through a diffraction grating. At what rate do the wave crests of the virtual photon pass through the diffraction grating?

The rate at which wave crests (cycles) pass by a given point in space is:

so = frequency of wave crests

 

Combining with the relation for the standing wave, the frequency of wave crests =  

This would be the matter wave frequency. Now what is the apparent wavelength of this matter wave frequency?

so  

 

This seems especially significant to me because using only this equation, the centripetal force equation, the Coulomb Attraction equation, and the equation for a circle, every quantity associated with one-electron atoms (Bohr radii, ionization energies, and spectral line frequencies) can be predicted with fairly good accuracy. In other words, quantum mechanics effects are not counter-intuitive, as we have always been told. They are exactly what we should expect.

Return to Home Page

Content of this paper may be freely used so long as credit is given to the author, Brian Stedjee

First publication date: September, 2003