Abstract
In the previous chapter we considered the concept of particles. This chapter we begin by introducing a number of basic concepts, which are essential for an understanding of wave phenomena in all parts of physics. We then will discuss the relation between waves and particles, which has played an important role in the development of modern physics. In 1925, Werner Heisenberg formulated his matrix mechanics. This is a quantum mechanics, which is derived from classical mechanics by introducing particle quantization. This theory has already been discussed in Section 58.21. Independently, in 1926, Erwin Schrödinger formulated an equivalent wave mechanics which is derived from wave quantization. The main objective of this chapter is to present a survey. This, together with the previous chapter, might help the reader to better understand many of the problems discussed later on. We thereby follow the fascinating line of development, which leads to the central problem of modern physics—the creation of a unified theory for all four interactions in nature. Quantum theory will be discussed in greater detail in Part V. Only a minimal program is presented here. Some interesting problems that we consider are:
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(i)
Spectrum of the hydrogen atom.
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(ii)
Quantum mechanical treatment of the harmonic oscillator in the context of Schrödinger’s wave mechanics.
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(iii)
Functional analytical deduction of Heisenberg’s uncertainty relation.
Except for atoms and emptyness nothing exists.
Demokrit (460 B.C.–371 B.C.)
There exists a limiting case of quantum theory which corresponds to classical particle physics, and there exists another which corresponds to classical wave mechanics. The alternatives which the limiting cases represent are not compatible. Bohr was therefore right when he called the duality between the two “pictures”—wave and particle—an example of complementarity.
Carl Friedrich von Weizsäcker (1973)
The last significant turn in quantum theory occurred after de Broglie’s discovery of matter waves in 1924, Heisenberg’s formulation of quantum mechanics in 1925, and Schrödinger’s general wave mechanical equation in 1926.
Wolfgang Pauli (1958)
Quantum theory so perfectly illustrates the fact that one might have understood a certain subject with complete clarity, yet at the same time knows that one can speak of it only allegorically and in pictures.
Werner Heisenberg (1901–1976)
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References
Reference to the Literature
Classical works: Planck (1900), Einstein (1905b), Heisenberg (1925), Schrödinger (1926).
Physical quantum theory: Heisenberg (1937, M), Pauli (1958, S), Landau and Lifšic (1962, M), Vols. 3,4, Bogoljubov and Širkov (1973, M), (1980, M), Itzykson and Zuber (1980, M), Lee (1981, M), Frampton (1987, M).
Mathematical quantum theory: von Neumann (1932, M), Van der Waerden (1980, M) (recommended as an introduction), Streater and Wightman (1964, M), Reed and Simon (1972, M), Vols. 1–4, Triebel (1972, M).
Genaral Reference to the Literature
General physics: Feynman, Leighton and Sands (1963, L) (Feynman Lectures, Vols. 1–3) (recommended as an introduction), Kittel (1965, L) (Berkeley Physics Course, Vols. 1–5), Orear (1966, M), Hänsel and Neumann (1972, M), Vols. 1–7, Lüscher (1980, M).
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Theoretical physics: Pauli (1973, M), Vols. 1–6, Macke (1962, M), Vols. 1–6, Kompanejec (1961, M), Ludwig (1978, M), Vols. 1–4, Weiler and Winkler (1974, M), Vols. 1–2, Greiner and Müller (1986, M), Vols. 1–10 (including recent advances in theoretical physics).
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Popular expositions about the development of modern physics, cosmology and biology: Riedl (1976, M), Bresch (1978, M), Sullivan (1979, M), Kippenhahn (1980, M), Unsold (1981, M), Fritzsch (1982, M), (1983, M), Sexl (1982, M), Ivanov (1983, M) (cybernetical methods in neuro-physiology, biology, cultural sciences, and the humanities), Henbest (1984, M), Trefil (1983, M), (1984), Taube (1985, M) (cf. p. 793).
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History of physics: von Laue (1950, M), Mehra (1982, M).
History of natural sciences: Wussing (1983, M).
Nobel lectures: The Nobel prizes (1954ff, M).
Unsolved problems in mathematical physics: Simon (1984, S).
Unsolved problems in mathematics: Browder (1976a).
The journals Nature and Scientific American inform about recent developments in science.
Survey about modern developments in mathematics: Jaffe (1984).
About current results in mathematics and the natural sciences one can consult the Lecture Notes in mathematics, biomathematics, chemistry, computer science, control and information sciences, economics, physics, and statistics. These lecture notes appear by Springer-Verlag.
Current developments in physics may also be found in the two series “Progress in Physics”, Birkhäuser, Boston and “Frontiers in Physics”, Benjamin, New York. Pursue the summer institute series “Les Houches (195Iff)”.
Fundamental formulas in physics: Menzel (1955, M).
Numerical recipies: Press (1986, M) (the art of scientific computing).
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Zeidler, E. (1988). Dualism Between Wave and Particle, Preview of Quantum Theory, and Elementary Particles. In: Nonlinear Functional Analysis and its Applications. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4566-7_3
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DOI: https://doi.org/10.1007/978-1-4612-4566-7_3
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