In electromagnetism, there is a notion called "Poynting vector."
It represents an electromagnetic energy flow current in vacuum space.
It is defined as a vector product of electric field E and magnetic field H.
In quantum mechanics, the electromagnetic wave is represented by the broadly prevailing notion of photon.
A photon has a definite energy hv.
The Poynting vector is well defined function of position and time, that is, S=S(x,y,z,t).
On the contrary, the quantum mechanical photon is ill defined regarding its position and time. It says only the energy the photon possesses.
Then here come my questions to you.
Is there anyone who can connect the above two kind of physical notions?
Is there anyone who can bridge the gap between the two features of light?
Regarding the Schrodinger equation: "There is no derivation of this equation. There is no proof of this equation. Scientists use this equation because it is useful." from page 9 of http://courses.chem.psu.edu/chem408/reading/activities/activity_2_QM.pdf
Schrodinger proposed his equation based on Max Plank's successful idea of quantum oscillators, which Plank modeled as masses on springs absorbing and re-emitting radiation. Plank did that in order to accurately predict the emission spectrum of a "black body emitter" such as a red hot iron or oven. The notion of quantum oscillators absorbing and re-emitting radiation would best be investigated at the source: Plank's paper on quantum oscillators.
The most cutting edge branch of this is currently Density Function Theory: Density functional theory - Wikipedia, the free encyclopedia
Yes, Planck succeeded in explaining the spectrum by assuming quantum energies of radiation based on harmonic oscillators. But at all, where are the electromagnetic harmonic oscillaors you mentioned? Usual textbooks do not tell us where they are. Are they involved in the atomic system that constitutes tha heated material? Can anybody indicate the position of the oscillators, or can anybody show what is the true character of the electromagnetic harmonic oscillators?
Since there is no derivation of the Scrodinger equation from first principles, there is a giant blank as you mentioned.
There are many people interested in deriving Schrodinger from first principles but it will take the next Einstein to figure that out.
Your question is connected to a more fundamental question - if, according to quantum mechanics, both electrons and photons have 'particle-like' and 'wave-like' features why did classical physics, which follows our common sense, day-to-day experience, saw the former as a particle and the second as a wave? The answer lies in the fact that the first is a fermion and the latter is a boson. So, only one electron can occupy one momentum state at a time, while many photons can occupy the same momentum state and when they do so they are in the so-called coherent state. This is what we see in a laser light where all the photons are moving in phase, giving a well-defined, macroscopic 'wave' with a single momentum, which is exactly what was proposed by Maxwell for electromagnetic waves.
Dear Prof Mitsuru, I have published a paper concerning your question: "Quantum uncertainty and Relativity", Progress in Physics, 2012, vol 2, pp 58-81; in this paper I concern the link between quantum uncertainty and Maxwell equations in the more general context of the link between relativity and quantum theory. I am writing presently another paper on this subject. If you like, it will be my pleasure send to you a preprint of this article when ready. Best regards. Sebastiano Tosto
Thanks to many poeple for your various opinions.
Dr. Hobbs, thank you for introducing many reference materiaals.
Dr. Datta, thank you for your explanation using the Fermion/Boson classification.
Dr. Tosto, thank you for showing your works which might have relation with my question. The honor is absolutely mine if I could have a look on your preprint paper when it is ready, Sir. I am looking forward to reading it. Remaining. M. Yamada