This is a very significant physical result because it tells us that the energy of a system described by a harmonic oscillator potential cannot have zero energy. Physical systems such as atoms in a solid lattice or in polyatomic molecules in a gas cannot have zero energy even at absolute zero temperature. The energy of the ground vibrational state is often referred to as “zero point vibration”. The zero point energy is sufficient to prevent liquid helium-4 from freezing at atmospheric pressure, no matter how low the temperature.
See:Quantum Harmonic Oscillator: Energy Minimum from Uncertainty Principle
It would be hard here to explain the way I see these things. In the way one can shift perspective, to think, that this measure of any “systemic reason” would ask that one consider the state of equilibrium?
It would be foolish to me for any science process to discount the value on how one can measure storms in space not to think that “such resonances” could have not found suitable actions as being represented in sociological correspondence.
Let us see how these great physicists used harmonic oscillators to establish beachheads to new physics.
Albert Einstein used harmonic oscillators to understand specific heats of solids and found that energy levels are quantized. This formed one of the key bridges between classical and quantum mechanics.
Werner Heisenberg and Erwin Schrödinger formulated quantum mechanics. The role of harmonic oscillators in this process is well known.
Paul A. M. Dirac was quite fond of harmonic oscillators. He used oscillator states to construct Fock space. He was the first one to consider harmonic oscillator wave functions normalizable in the time variable. In 1963, Dirac used coupled harmonic oscillators to construct a representation of the O(3,2) de Sitter group which is the basic scientific language for two-mode squeezed states.
Hediki Yukawa was the first one to consider a Lorentz-invariant differential equation, with momentum-dependent solutions which are Lorentz-covariant but not Lorentz-invariant. He proposed harmonic oscillators for relativistic extended particles five years before Hofstadter observed that protons are not point particles in 1955. Some people say he invented a string-model approach to particle physics.
Richard Feynman was also fond of harmonic oscillators. When he gave a talk at the 1970 Washington meeting of the American Physical Society, he stunned the audience by telling us not to use Feynman diagrams, but harmonic oscillators for quantum bound states. This figure illustrates what he said in 1970.
We are still allowed to use Feynman diagrams for running waves. Feynman diagrams applicable to running waves in Einstein’s Lorentz-covariant world. Are Feynman’s oscillators Lorentz-covariant? Yes in spirit, but there are many technical problems. Then can those problems be fixed. This is the question. You may be interested in reading about this subject: Lorentz group in Feynman’s world.
Can harmonic oscillators serve as a bridge between quantum mechanics and special relativity
To consider such geometrical form “as the sphere,” to have encouraged collapse, and find a resulting behaviour as signalling a change overwrought by influences that will insight idealizations to division and the idea that “no” global consideration is present.
While one may debate the idea of the classification of democracies in the 167 countries around the world, a consensus to quality control of information is insinuated. So now moving beyond “the border” to lesser degrees of, while there is no offering of what the idea of democratic institutions in the free countries of the world could be related too. It’s measure in the degrees thereof.
While I had offered “in bold” the understanding, they( should I offer by name?) are quick to point out in rebuttal, by an offering to discount the very source of this consideration. I am all for further dialogue, but it looks like that won’t happen.
So how does it look, as a spherical realization, that SOHO measure in terms of predicting an “outcome of weather” could not have found “early warnings” to possible outcomes in the evolution of the planet it’s electrical grids and power usage, telecommunications, and the events thereof?
You had to know that Plato “saw further” by understanding the examples of the sun, as a source of “seeing beyond the shadows of the cave.” Of knowing, that one could be “free of the chains that bind.”
No where does this say it is easy to overcome. The sociological and psychological behaviour that evolves in that “spherical engage”, but that it is always the life struggle to get back to the light. One had to be fully aware of the topological translation of the relationship between the inner/outer and the reductionist move to what is self evident. There is no way for one to be aware of the analysis and the final outcome without knowing the way in which one could move to such a result, without knowing the wider perspective that is held about life.