# The Development of Quantum Mechanics

# The Development of Quantum Mechanics

*Overview*

Quantum mechanics describes the relationship between energy and matter on an atomic and subatomic scale. At the beginning of the twentieth century, German physicist Maxwell Planck (1858-1947) proposed that atoms absorb or emit electromagnetic radiation in bundles of energy termed quanta. This quantum concept seemed counter-intuitive to well-established Newtonian physics. Advancements associated with quantum mechanics (e.g., the uncertainty principle) also had profound implications for philosophical and scientific arguments concerning the limitations of human knowledge.

*Background*

The classical model of the atom that emerged during the last decade of the nineteenth century and the early years of the twentieth century was similar to the Copernican model of the solar system, where, just as planets orbit the sun, electrically negative electrons move in orbits about a relatively massive, positively charged nucleus. Most importantly, in accordance with Newtonian theory, the classical models allowed electrons to orbit at any distance from the nucleus. Problems with these models, however, continued to vex the leading physicist of the nineteenth century. The classical models predicted that when, for example, a hydrogen atom was heated, it should produce a continuous spectrum of colors as it cooled. Nineteenth-century spectroscopic experiments, however, showed that hydrogen atoms produced only a portion of the spectrum. Moreover, studies on electromagnetic radiation by physicist James Clark Maxwell (1831-1879) predicted that an electron orbiting around the nucleus, according to Newton's laws, would continuously lose energy and eventually fall into the nucleus.

Planck proposed that atoms absorb or emit electromagnetic radiation only in certain units or bundles of energy termed quanta. The concept that energy existed only in discrete and defined units seemed counter-intuitive, that is, outside of the human experience with nature. Regardless, Planck's quantum theory, which also asserted that the energy of light was directly proportional to its frequency, proved a powerful theory that accounted for a wide range of physical phenomena. Planck's constant relates the energy of a photon with the frequency of light. Along with constant for the speed of light, Planck's constant (*h* = 6.626 × 10^{-34} Joule-second) is a fundamental constant of nature.

Prior to Planck's work, electromagnetic radiation (light) was thought to travel in waves with an infinite number of available frequencies and wavelengths. Planck's work focused on attempting to explain the limited spectrum of light emitted by hot objects and to explain the absence of what was termed the "violet catastrophe," predicted by nineteenth-century theories developed by physicists Wilhelm Wien (1864-1928) and John William Strutt Rayleigh (1842-1919).

Danish physicist Niels Bohr (1885-1962) studied Planck's quantum theory of radiation and worked in England with physicists J. J. Thomson (1856-1940) and Ernest Rutherford (1871-1937), improving their classical models of the atom by incorporating quantum theory. During this time, Bohr developed his model of atomic structure. To account for the observed properties of hydrogen, Bohr proposed that electrons existed only in certain orbits and that, instead of traveling between orbits, electrons made instantaneous quantum leaps or jumps between allowed orbits. According to the Bohr model, when an electron is excited by energy it jumps from its ground state to an excited state (i.e., a higher energy orbital). The excited atom can then emit energy only in certain (quantized) amounts as its electrons jump back to lower energy orbits located closer to the nucleus. This excess energy is emitted in quanta of electromagnetic radiation (photons of light) that have exactly the same energy as the difference in energy between the orbits jumped by the electron.

The electron quantum leaps between orbits proposed by the Bohr model accounted for Plank's observations that atoms emit or absorb electromagnetic radiation in quanta. Bohr's model also explained many important properties of the photoelectric effect described by Albert Einstein (1879-1955).

*Impact*

The development of quantum mechanics during the first half of the twentieth century replaced classical Copernican-like atomic models of the atom. Using probability theory, and allowing for a wave-particle duality, quantum mechanics also replaced classical mechanics as the method by which to describe interactions between sub-atomic particles. Quantum mechanics replaced electron "orbitals" of classical atomic models with allowable values for angular momentum (angular velocity multiplied by mass) and depicted electron position in terms of probability "clouds" and regions.

When Planck started his studies in physics, Newtonian or classical physics seemed fully explained. In fact, Planck's graduate advisor once claimed that there was essentially nothing new to discover in physics. By 1918, however, the importance of quantum mechanics was recognized and Planck received the Nobel Prize for Physics. The philosophical implications of quantum theory seemed so staggering, however, that Planck himself admitted that he did not fully understand the theory. In fact, Planck initially regarded the development of quantum mechanics as a mathematical aberration or temporary answer to be used only until a more intuitive or commonsense model was developed.

Despite Planck's reservations, however, Einstein's subsequent Nobel prize-winning work on the photoelectric effect was heavily based on Planck's theory. Expanding on Planck's explanation of blackbody radiation, Einstein assumed that light was transmitted as a stream of particles termed photons. By extending the well-known wave properties of light to include a treatment of light as a stream of photons, Einstein was able to explain the photoelectric effect.

The Bohr model of atomic structure was published in 1913 and Bohr's work earned a Nobel Prize in 1922. Bohr's model of the hydrogen atom proved to be insufficiently complex to account for the fine detail of the observed spectral lines. However, Prussian physicist Arnold Sommerfeld (1868-1951) provided refinements (e.g., the application of elliptical, multi-angular orbits) that explained the fine-structure of the observed spectral lines.

Later in the 1920s, the concept of quantization and its application to physical phenomena was further advanced by more mathematically complex models, based on the work of French physicist Louis Victor de Broglie (1892-1987) and Austrian physicist Erwin Schrödinger (1887-1961), that depicted the particle and wave nature of electrons. De Broglie showed that the electron was not merely a particle but a wave form. This proposal led Schrödinger to publish his wave equation in 1926. Schrödinger's work described electrons as a "standing wave" surrounding the nucleus, and his system of quantum mechanics is called wave mechanics. German physicist Max Born (1882-1970) and English physicist P.A.M Dirac (1902-1984) made further advances in defining subatomic particles (principally the electron) as a wave rather than a particle, and reconciled portions of quantum theory with relativity theory.

Working at about the same time, German physicist Werner Heisenberg (1901-1976) formulated the first complete and self-consistent theory of quantum mechanics. Matrix mathematics was well-established by the 1920s, and Heisenberg applied this powerful tool to quantum mechanics. In 1926 Heisenberg put forward his uncertainty principle, which states that two complementary properties of a system, such as position and momentum, can never both be known exactly. This proposition helped cement the dual nature of particles (e.g., light can be described as having both wave and particle characteristics). Electromagnetic radiation—one region of the spectrum that comprises visible light—is now understood as having both particle and wave-like properties.

In 1925 Austrian-born physicist Wolfgang Pauli (1900-1958) published the Pauli exclusion principle, which states that no two electrons in an atom can simultaneously occupy the same quantum state (i.e., energy state). Pauli's specification of spin (+1/2 or -1/2) established that two electrons in any suborbital have differing quantum numbers (a system used to describe the quantum state). This insight made completely understandable the structure of the periodic table in terms of electron configurations (i.e., the energy related arrangement of electrons in energy shells and suborbitals).

In 1931 American chemist Linus Pauling (1901-1994) published a paper that used quantum mechanics to explain how two electrons, from two different atoms, are shared to make a covalent bond between the two atoms. Pauling's work provided the connection needed in order to fully apply the new quantum theory to chemical reactions.

Quantum mechanics posed profound questions for scientists and philosophers. The concept that particles such as electrons make quantum leaps from one orbit to another, as opposed to simply moving between orbits, seemed counter-intuitive. Like much of quantum theory, the proofs of how nature works at the atomic level are mathematical. Bohr himself remarked, "Anyone who is not shocked by quantum theory has not understood it."

The rise of the importance and power of quantum mechanics carried important philosophical consequences. When misapplied to larger systems—as in the famous paradox of Schrödinger's cat—quantum mechanics could be misinterpreted to make bizarre predictions (i.e., a cat that is simultaneously dead and alive). On the other hand, quantum mechanics made possible important advances in cosmological theory.

Quantum and relativity theories strengthened philosophical concepts of complementarity, wherein phenomenon can be looked upon in mutually exclusive yet equally valid perspectives. In addition, because of the complexity of quantum relationships, the rise of quantum mechanics fueled a holistic approach to explanations of physical phenomena. Following the advent of quantum mechanics, the universe could no longer be explained in terms of Newtonian causality, but only in terms of statistical, mathematical constructs.

In particular, Heisenberg's uncertainty principle asserts that knowledge of natural phenomena is fundamentally limited—to know one part allows another to move beyond recognition. Quantum mechanics, particularly in the work of Heisenberg and Schrödinger, also asserted an indeterminist (no preferred frame of reference) epistemology, suggesting that human knowledge itself is limited by inescapable aspects of incompleteness and randomness.

Fundamental contradictions with long accepted Newtonian causal and deterministic theories made even the leading scientists of the day resistant to the philosophical implications of quantum theory. Einstein argued against the seeming randomness of quantum mechanics by asserting, "God does not play dice!" Bohr and others defended quantum theory with the gentle rebuttal that one should not "prescribe to God how He should run the world."

**K. LEE LERNER**

*Further Reading*

Bohr, Niels. *The Unity of Knowledge.* New York: Doubleday, 1955.

Feynman, Richard P. *The Character of Physical Law.* Cambridge: MIT Press, 1965.

Feynman, Richard P. *QED: The Strange Theory of Light and**Matter.* Princeton, NJ: Princeton University Press, 1985.

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