The expression E = h × f is misleading because it implies the distribution of a photon quantum over 299 792 458 m, while the expression E = (h × c)/λ enables us to explain the particle-wave duality

2021 ◽  
Vol 34 (4) ◽  
pp. 564-577
Author(s):  
Reiner Georg Ziefle

The two equations E = h × f and E = (h × c)/λ for the quantum of energy of electromagnetic radiation provide the same result but describe electromagnetic radiation very differently. E = (h × c)/λ describes the quantum of energy of electromagnetic radiation to be located already in one wavelength and therefore like a particle. E = h × f describes the quantum of energy distributed over 299 792 458 m and therefore like a wave. To obtain h × f for the quantum of energy, we have to refer the quantum of energy to 299 792 458 m. Only then we obtain from E = (h × c)/(299 792 458 m), as the distance of 299 792 458 m of the velocity c is cancelling out now, E = h × 1/s = h × Hz, which is the precondition to obtain the correct value for the quantum of energy by multiplying Planck’s constant h by the frequency f. This already indicates the necessity of today's physics to have to speak of a particle-wave duality. It turns out that electromagnetic radiation consists of the first wavelength that carries the quantum of energy and behaves like a particle, which today is called “photon,” and a few following wavelengths that do not carry a further quantum of energy and behave like a wave, which today is called “electromagnetic wave.” By this knowledge, the particle-wave duality vanishes, and we obtain one single physical phenomenon, which I call “photon-wave.” The strange behavior of quantum objects at a single slit, at double-slits, and at beam splitters can now be understood in a causal way. “God does not play dice!” Einstein was right.

2016 ◽  
Vol 24 (1) ◽  
pp. 43-69 ◽  
Author(s):  
Stephen Bruce Sontz

Abstract Toeplitz quantization is defined in a general setting in which the symbols are the elements of a possibly non-commutative algebra with a conjugation and a possibly degenerate inner product. We show that the quantum group SUq(2) is such an algebra. Unlike many quantization schemes, this Toeplitz quantization does not require a measure. The theory is based on the mathematical structures defined and studied in several recent papers of the author; those papers dealt with some specific examples of this new Toeplitz quantization. Annihilation and creation operators are defined as densely defined Toeplitz operators acting in a quantum Hilbert space, and their commutation relations are discussed. At this point Planck’s constant is introduced into the theory. Due to the possibility of non-commuting symbols, there are now two definitions for anti-Wick quantization; these two definitions are equivalent in the commutative case. The Toeplitz quantization introduced here satisfies one of these definitions, but not necessarily the other. This theory should be considered as a second quantization, since it quantizes non-commutative (that is, already quantum) objects. The quantization theory presented here has two essential features of a physically useful quantization: Planck’s constant and a Hilbert space where natural, densely defined operators act.


Author(s):  
Robert H. Swendsen

A black body is a perfect absorber of electromagnetic radiation. The energy spectrum was correctly calculated by Max Planck under the assumption that the energy of light waves only came in discrete multiples of a constant (called Planck’s constant) times the frequency. This was perhaps the first achievement of quantum mechanics. The derivation is presented here. The purpose of the current chapter is to calculate the spectrum of radiation emanating from a black body. The calculation was originally carried out by Max Planck in 1900 and published the following year. This was before quantum mechanics had been invented, or perhaps it could be regarded the first step in its invention.


1976 ◽  
Vol 31 (12) ◽  
pp. 1517-1519 ◽  
Author(s):  
P. K. Shukla ◽  
M. Y. Yu ◽  
S. G. Tagare

Abstract We show analytically that the nonlinear coupling of a large amplitude electromagnetic wave with finite amplitude ion fluctuations leads to filamentation. The latter consists of striations of the electromagnetic radiation trapped in depressions of the plasma density. The filamentation is found to be either standing or moving normal to the direction of the incoming radiation. Criteria for the existence of localized filaments are obtained. Small amplitude results are discussed.


2019 ◽  
Vol 7 (3) ◽  
pp. 253-261
Author(s):  
Hartono Bancong ◽  
Ana Dhiqfaini Sultan ◽  
Subaer Subaer ◽  
Muris Muris

The photoelectric effect experiment generally uses a very sophisticated and expensive apparatus. Some high schools and even universities in Indonesia cannot afford to conduct this experiment because of the high price of the apparatus. The purpose of this study was to develop a user-friendly, and cost-effective teaching aids which can be used to demonstrate the concepts of modern physics related to the photoelectric effect. The stages of this study employed the Four-D model, namely define, design, develop, and disseminate. Based on experts and practitioner evaluation, the developed teaching aids and practicum devices of photoelectric effect experiment were found to be valid and reliable. The results of the experiment by using this developed teaching aids of the photoelectric effect showed that there is a linear relationship between the stopping potential and the frequency of light emitted by the LED. These results are consistent with Millikan's experimental results, the first physicist who succeed in proving Einstein's hypothesis of the photoelectric effect, that in the photoelectric effect the stopping potential does not depend on the intensity of light but depends only on the frequency of light. In this study, the Planck’s constant value obtained is 6.408x10-34 J.s. Although this value is slightly smaller than the accepted value of Planck's constant that is 6.626x10-34 J.s, it is good enough considering the instrumental error occurred during the measurement of current and voltage. Furthermore, the students’ perception of the developed teaching aids and practicum devices of the photoelectric effects experiment are 74.9% (good) and 80.2% (very good), respectively. This indicates that the photoelectric effect experiment teaching aids and practicum devices that have been developed can be used to demonstrate and prove the concepts of modern physics related to the photoelectric phenomena correctly.Keywords: Teaching Aids, Photoelectric Effect, Students’ Perception


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