When Victor-Louis de Broglie linked the wave nature of matter to the fundamental size and structure of atoms, the stage was set for quantum physics to enter a fantastic and bizarre realm of discovery. The realization that the wavelength of the electron determined an atoms size provided the seeds that led Max Born (through Schrödinger’s equation) to a startling conclusion. He realized that there was a connection between quantum wavelength distributions (probabilities) of electrons and their particulate behavior; that is wave-particle duality and wave-probability go together. The implications were enormous as the whole of quantum physics became probabilistic in nature. Additionally, here was a better way to probe the quantized or granular nature of reality.
This granular characteristic has roots in the very make up of reality itself. Probing the tiniest boundaries of existence, a place where the plank scale rules, it is possible to glimpse mysterious and fundamental interactions that ultimately describe this granular reality. For example, by observing the dynamic relationship between electrons and atomic nuclei we gain some understanding of the origins to this quantized or granular existence. Among the various complex quantum forces, these two seem to stand out together bound in eternal conflict. But one that results in the very reality we live in.
The kinetic energy of an electron searches out the lowest energy and “seeks” to expand out and away from the nucleus while the attractive force – the potential energy of the nucleus “pulls” at the electron. A balance is reached between these two forces and the electron spreads itself throughout this specified region (which turns out to be around 10-10 m). As nuclei increase in size, they pull electrons closer to the nucleus thus forcing them into a higher kinetic state allowing “space” for more electrons to occupy up to a maximum region of balance (of charges). The last electron to fill the imbalance of forces will eventually fall into the same region as the electron of the smallest nucleus does (hydrogen)-10-10m; hence all atoms are actually similar in size.
Ultimately, the balance between the kinetic energy of the electron and the potential energy of the atomic nucleus provide a natural backdrop from where quantum behavior can have wave like properties. As an electron distributes itself in three dimensions at the point of balance, its wavelength is “focused” or bound in an area around the nucleus. However, because of the diffuse distribution of a wave, even a fixed wave, it “oscillates” and behaves probabilistically. That is you can not readily localize it to one spot- it is nonlocal.
Interestingly, depending upon the electrons excitement the wavelength will oscillate around the nucleus at varying frequencies. For example, using the Hydrogen atom Kenneth Ford (The Quantum World) describes the resulting phenomena stating: “This behavior is reminiscent of the vibration of a violin string in its fundamental mode and in its higher harmonics. The lowest vibration frequency of a string held fixed at its two ends has one-half wavelength over the end of the string. The second harmonic is one in which there is a full wavelength over the length of the string…And so on. It is the nature of the rules governing sound that the second harmonic is twice the frequency of the fundamental…and so on…the frequencies of vibration of the violin string are quantized. A string of given length and tension vibrates only at a discrete set of frequencies.”
In essence, the observed quantization of atoms is, in some ways analogous to different lengths of vibrating waves with their combined set of specific frequencies. Schrödinger provided the equation that mathematically yielded the observed quantized energies, which thereby supported de Broglie’s wave-matter theory. This salient topic, from a quantum point of view, helps broaden ones perspective concerning the nature of reality and opens the way to ever stranger domains.
Ref Ford, K the quantum world. Havard Univ Press.Massachusetts, USA.2004