Abstract
From fundamental physics we know well that a substance consists of molecules and atoms. Depending on the character and intensity of the interaction between atoms and molecules, a substance is in one of the following aggregate states: gas, liquid, solid, or plasma. Quantum electronics deals with all of these states, and we consider them in the order of an increasing degree of interaction between particles. We begin with an excursus on an isolated atom.
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Notes
- 1.
Max Planck (1858–1947) was a German physicist, the founder of quantum theory, and a foreign honorary member of the Soviet Academy of Sciences. In 1918 he received the Nobel Prize in Physics. The German Physical Society named its highest award the Plank Medal in his honor. He was also a remarkable pianist and a climber.
- 2.
Louis de Broglie (1892–1987) was a French physicist and one of the founders of quantum mechanics. In 1929 he received the Nobel Prize in Physics. In 1933 he was elected as a member of the French Academy of Science. He was a founder of the Center of Research on Applied Mathematics at the Poincare Institute for strengthening the connections between physics and applied mathematics.
- 3.
Euclid (circa 365 BC–circa 300 BC) was an ancient Greek mathematician who worked in Alexandria. His main work, Principles (which includes 15 books), contains descriptions of planimetry, stereometry, and a series of problems related to number theory, algebra, the general theory of ratios, and methods of area and volume determination, including the elements of limits (the exhaustion method).
- 4.
Erwin Schrödinger (1887–1961) was an Austrian physicist–theorist and one of the founders of quantum theory. In 1933 he received the Nobel Prize in Physics, and in 1937 he was awarded the Max Plank Medal by the German Physical Society.
- 5.
Later, we discuss the problems of simultaneous measurement of physical variables.
- 6.
In (1.6) and subsequently, dr is the volume element of the selected coordinate system—for instance, dx, dy, dz.
- 7.
The envelope of the wave packet moves in the space with the group velocity \( {V}_{\mathrm{gr}}=\frac{d\omega}{d k}=\frac{1}{\hslash}\frac{d W}{d k} \).
- 8.
Werner Heisenberg (1901–1976) was a German physicist–theorist and one of the creators of quantum mechanics. He was awarded the Nobel Prize in Physics in 1932, the Max Plank Medal by the German Physical Society in 1933, a bronze medal by the National Academy of Sciences of the USA in 1964, and the Nils Bohr International Gold Medal by the Danish Society of Construction, Electrical and Mechanical Engineers in 1970.
- 9.
This term was introduced at the end of the nineteenth century by J.R. Rydberg (1854–1919), a Swedish physicist, mathematician, and member of the Swedish Academy of Sciences (1919). A definite energy value—the energy level—corresponds to each term. Rydberg offered the formula to determine the wavelength of any spectral line. In 1980 he introduced the physical constant that would eventually be named after him.
- 10.
The name “fianit” comes from the abbreviation “FIAN”, which stands for the Physical Institute of the Academy of Sciences (Russia), where it was synthesized for the first time. However, this name is not used beyond the former USSR.
- 11.
Nowadays, an “amorphous solid” is considered to be the overarching concept and “glass” is a more special case; glass is an amorphous solid that transforms into a liquid upon heating through the glass transition. The glass transition is a reversible transition in amorphous materials from a hard and relatively brittle state into a molten or rubber-like state.
- 12.
Ralph Kronig was a German–American physicist (1904–1995). He is noted for the discovery of particle spin and for his theory of x-ray absorption spectroscopy. His theories include the Kronig–Penney model, the Coster–Kronig transition, and the Kramers–Kronig relation.
- 13.
William Penney (1909–1991) was a British mathematician, professor of mathematical physics at Imperial College, London, and later the Rector of Imperial College.
- 14.
In mathematics, Eq. (1.39) is known as the Hill equation, the form of solutions to which is defined by the Floquet theorem.
- 15.
The exact solution has a complicated form. The mentioned equation is obtained if b → 0, V0 → ∞ at the constant value of bV0.
- 16.
The abbreviation “tr” comes from “trace”; sometimes the abbreviation “sp” (from “spoor”) is used.
- 17.
Wolfgang Pauli (1900–1958) was an Austrian theoretical physicist and one of the founders of quantum mechanics and relativistic quantum field theory. In 1945 he received the Nobel Prize in Physics, and in 1958 he was awarded the Max Plank Medal by the German Physical Society. He was elected to membership of the Swiss Physical Society, the American Physical Society, and the American Association of Fundamental Sciences, and foreign membership of the Royal Society.
- 18.
Enrico Fermi (1901–1954) was an Italian physicist and one of the founders of nuclear physics. He received the Nobel Prize in Physics in 1938. He created the first nuclear reactor and in 1942 discovered the chain reaction. The 100th element in the Mendeleev table—fermium—was named in his honor. In the USA, the Institute for Nuclear Studies in Chicago was renamed the Enrico Fermi Institute for Nuclear Studies in 1955, and the Enrico Fermi Award was established in 1956.
- 19.
Satyendra Bose (1894–1974) was an Indian physicist from Bengal, who specialized in mathematical physics and was one of the founders of quantum statistics. He was elected to membership of the Royal Society in 1958.
- 20.
Ludwig Boltzmann (1844–1906) was an Austrian physicist and one of the founders of statistical physics. His scientific interests covered almost all fields of physics and some areas of mathematics. He authored publications in mathematics, mechanics, hydrodynamics, elasticity theory, electromagnetic field theory, optics, thermodynamics, and kinetic theory of gases.
- 21.
It should be taken into account that Ni and (1.65) have a sense of probability that states with energy Wi are occupied.
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Shtykov, V.V., Smolskiy, S.M. (2020). Excursus on the Atomic–Molecular Theory of Substance. In: Introduction to Quantum Electronics and Nonlinear Optics. Springer, Cham. https://doi.org/10.1007/978-3-030-37614-7_1
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DOI: https://doi.org/10.1007/978-3-030-37614-7_1
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