In Schrodinger’s wave equation for the electron, the wave function (ψ) could represent the very substance of energy that thickens as frequency increases. Here the “center of mass” of the electron itself is no longer a point but dispersed. But the “center of mass” of the whole atom can be a point.
I do not see Quantum Mechanics as a radical break from the past. In the past a particle, such as, an atom, was perceived as a solid billiard ball whose internal structure was a black box. Quantum mechanics is simply an advance in science that is looking more closely at that black box. The mass of an atom is concentrated in the nucleus, except for some mass scattered around the nucleus in the form of the electrons. This shows that the mass “dilutes” into electromagnetic substance. The mathematics that is trying to explain this is complicated.
The mathematics of wave-particle duality of De Broglie and the Schrodinger’s equation is based on the analogy between the behavior of light of very short wavelength and the behavior of ordinary particles of matter. This means that matter could be an extension of the upper end of the electromagnetic spectrum.
The new discovery is that that the “center of mass” of a particle like electron cannot be determined precisely because it is dispersed. Classical Newtonian mechanics is based on precise point-like “center of mass.” But at very small scales, a “particle” seems to have a more diffused picture, and classical mechanics can no longer be used. At still smaller scales, we may find the nucleons to be diffused as well.
The location of a particle is determined by the location of its “center of mass”. If this location cannot be determined exactly, and is described in terms of probability, then the “center of mass” itself is dispersed. This gives the picture of a particle of variable energy density.
The Schrodinger’s equation treats electron as if it is a “wave” made of thick elastic fluid. This wave is not moving in some medium. It is the “medium” itself moving as a wave. It becomes “thicker” with higher amplitude. The amplitude is a measure of its thickness. The rising and falling “thickness” is made up of rising and falling frequency. The spectral line is the peak of this frequency. It is like a resonance; but this is a traveling “resonance”. The electron is an energy resonance moving around the nucleus of an atom.
In classical mechanics, the density of matter means the “concentration of atoms” in a certain volume. The density of individual atomic particle is determined by its mass number in the periodic table. The density of individual sub-atomic particle is then determined by its wave function. Beyond the density of the sub-atomic particle is the energy density of the electromagnetic quantum, which is based on simple frequency.
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