g is true.
If we subsequently combine equals from Equation (13) and Equation (14), we obtain:
Here, the left half is the energy contained within the electron. This energy is emitted as multiple photons when it is externally emitted. The right half of this equation is the sum of all of this photon energy as represented by the frequency of a photon when converted into a single photon. Fundamentally these two types of energy have different characteristics, but from a quantitative perspective, it is possible to combine them as equals.
Incidentally, an electron’s Compton wavelength is represented by the following equation.
The Planck constant can be defined as follows from Equation (16).
Incidentally, Equation (13) can be written as follows.
is the wavelength of a photon with energy ,but when Equation (17) is taken into account, Equation (18) can be written as follows.
Comparing Equation (17) and Equation (18), it is evident that in Equation (18) matches the electron’s Compton wavelength.
Thus, if we call the Compton frequency, and rewrite it as, then Equation (18) becomes as follows.
Next, let’s consider the case where the energy of the photon is not but rather.
The following relation holds between and. (Naturally, m and are not the mass of the photon.)
At this time, the following relation holds.
From Equation (21) and Equation (22) it is evident that all photon energies can be described using the following formula.
We next substitute the following values for physical quantities in .
By doing so, becomes as follows.
Meanwhile, the Planck constant has the following value .
and h are a perfect match. The currently known values for or were not determined through experimentation. was determined through precise calculations from Rydberg constant formulas, and was obtained by substituting in the formula
Based on measured data from theoretical formulas or experiments designed to represent the fundamental laws of physics, many fundamental physical constants are being adjusted to avoid conflicts from arising between these constants. Because the formula to determine an electron’s Compton wavelength is, naturally the modified version of this Equation (17) is true. When we logically rewrite the Planck constant from Equation (11) into Equation (12) to include the frequency of a photon, we notice that non-frequency components are always constant, and this constant can be rewritten (defined) as h, a new constant.
While differing from historical development, we interpret (17) to mean not only that “and h are the same” but to mean that “is defined as h for sake of simplicity”. Therefore, this paper does not claim the discovery of any relationship in Equation (17). However, because the Planck constant has historically been presumed to be a comparative constant used in Planck’s harmonic oscillator energy quantum hypothesis and Einstein’s light quantum hypothesis, it has taken on the image of being a discovered universal constant.
According to existing theory, Equation (11) and Equation (12) have been thought to have similar importance. However, according to our discussion, Equation (11) is the more fundamental of the two. Equation (12) is merely Equation (11) rewritten to also include frequency. The right side of Equation (19), the product of the physical quantities except for frequency, is a steady value.
In this paper, we conclude that, theoretically, the Planck constant h first comes into existence as a constant once we agree to name as h. However, we have historically overlooked this agreement (definition). Then, the energy of a photon was presumed from the beginning to be proportional with its frequency; this proportional constant was named the Planck constant, and was considered to be a mysterious universal constant that ruled over the micro-world which could not be explained by classical mechanics.
There is no problem with introducing h to simplify equations, but quantum mechanics is not affected even if there is no symbol h. Although it is bothersome, one can get by writing instead of h. If one wishes to retain the Planck constant as a