Quantum Mechanics

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Quantum Mechanics

Theoretical implications of quantum mechanics

Quantum mechanics is a fundamental part of theoretical physics that involves the theory used to provide an understanding of the behavior of microscopic particles such as electrons and atoms. More

importantly, quantum mechanics describes the relationships between energy and matter on atomic and subatomic scales. Thus, it replaces classical mechanics and electromagnetism when dealing with these very small scales. Quantum mechanics is used in such scientific fields as computational chemistry, condensed matter, molecular physics, nuclear physics, particle physics, and quantum chemistry.

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. Ultimately, advancements associated with quantum mechanics (e.g., the uncertainty principle) also had profound implications with regard to the philosophical scientific arguments regarding the limitations of human knowledge.

Planck proposed that atoms absorb or emit electromagnetic radiation in defined and discrete units (quanta). Planck’s quantum theory also asserted that the energy of light was directly proportional to its frequency, and this proved a powerful observation 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 the constant for the speed of light (c), Planck’s constant (h = 6.626 x 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 Prussian physicist Wilhelm Wien (1864-1928) and English physicist Baron (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 German-American mathematician and physicist Albert Einstein (1879-1955).

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 subatomic particles. Quantum mechanics replaced electron orbitals of classical atomic models with allowable values for angular momentum (angular velocity multiplied by mass) and depicted electrons position in terms of probability clouds and regions.

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 Schrodinger (1887-1961) that depicted the particle and wave nature of electrons. De Broglie showed that the electron was not merely a particle but a waveform. This proposal led Schrodinger to publish his wave equation in 1926. Schrodinger’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 the subatomic particles (principally the electron) as a wave rather than as a particle and in reconciling 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. Matrixmathematics was well-established by the 1920s, and Heisenberg applied this powerful tool to quantum mechanics. In 1926, Heisenberg put forward his uncertainty principle that 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 of which 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 that 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) on an electron gave the two electrons in any suborbital differing quantum numbers (a system used to describe the quantum state) and 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 making quantum leaps from one orbit to another, as opposed to simply moving between orbits, seems counter-intuitive, that is, outside the human experience with nature. 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.”

Quantum results

Quantum mechanics requires advanced mathematics to give numerical predictions for the outcome of measurements. However, one can understand many significant results of the theory from the basic properties of the probability waves. An important example is the behavior of electrons within atoms. Since such electrons are confined in some manner, scientists expect that they must be represented by standing waves that correspond to a set of allowed frequencies. Quantum mechanics states that for this new type of wave, its frequency is proportional to the energy associated with the microscopic particle. Thus, one reaches the conclusion that electrons within atoms can only exist in certain states, each of which corresponds to only one possible amount of energy. The energy of an electron in an atom is an example of an observable which is quantized, that is it comes in certain allowed amounts, called quanta (like quantities).

When an atom contains more than one electron, quantum mechanics predicts that two of the electrons both exist in the state with the lowest energy, called the ground state. The next eight electrons are in the state of the next highest energy, and so on following a specific relationship. This is the origin of the idea of electron shells, or orbits, although these are just convenient ways of talking about the states. The first shell is filled by two electrons, the second shell is filled by another eight, etc. This explains why some atoms try to combine with other atoms in chemical reactions.

This idea of electron states also explains why different atoms emit different colors of light when they are heated. Heating an object gives extra energy to the atoms inside it and this can transform an electron within an atom from one state to another of higher energy. The atom eventually loses the energy when the electron transforms back to the lower-energy state. Usually the extra energy is carried away in the form of light which is said was produced by the electron making a transition, or a change of its state. The difference in energy between the two states of the electron (before and after the transition) is the same for all atoms of the same kind. Thus, those atoms will always give off a wavelength and frequency of light (i.e.,

KEY TERMS

Classical mechanics— A collection of theories, all derived from a few basic principles, that can be used to describe the motion of macroscopic objects.

Macroscopic— This term describes large-scale objects like those humans directly interact with on an everyday basis.

Microscopic— This term describes extremely small-scale objects such as electrons and atoms with which humans seldom interact on an individual basis as humans do with macroscopic objects.

Observable— A physical quantity, like position, velocity or energy, which can be determined by a measurement.

Planck’s constant— A constant written as h, which was introduced by Max Planck in his quantum theory and that appears in every formula of quantum mechanics.

Probability— The likelihood that a certain event will occur. If something happens half of the time, its probability is 1/2 = 0.5 = 50%.

Quantum— The amount of radiant energy in the different orbits of an electron around the nucleus of an atom.

Wave— A motion, inwhichenergy and momentum is carried away from some source, which repeats itself in space and time with little or no change.

color) that corresponds to that energy. Another element’s atomic structure contains electron states with different energies (since the electron is confined differently) and so the differing energy levels produce light in other regions of the electromagnetic spectrum. Using this principle, scientists can determine which elements are present in stars by measuring the exact colors in the emitted light.

Quantum mechanics theory has been extremely successful in explaining a wide range of phenomena, including a description of how electrons move in materials (e.g., through chips in a personal computer). Quantum mechanics is also used to understand superconductivity, the decay of nuclei, and how lasers work.

Theoretical implications of quantum mechanics

The standard model of quantum physics offers an theoretically and mathematically sound model of particle behavior that serves as an empirically validated middle-ground between the need for undiscovered hidden variables that determine particle behavior, and a mystical anthropocentric universe where it is the observations of humans that determine reality. Although the implications of the latter can be easily dismissed, the debate over the existence of hidden variables in quantum theory remained a subject of serious scientific debate during the twentieth century and, now, early into the twenty-first century. Based upon everyday experience, well explained by the deterministic concepts of classical physics, it is intuitive that there be hidden variables to determine quantum states. Nature is not, however, obliged to act in accord with what is convenient or easy to understand. Although the existence and understanding of heretofore hidden variables might seemingly explain Einstein’s “spooky” forces, the existence of such variables would simply provide the need to determine whether they, too, included their own hidden variables.

Quantum theory breaks this never-ending chain of causality by asserting (with substantial empirical evidence) that there are no hidden variables. Moreover, quantum theory replaces the need for a deterministic evaluation of natural phenomena with an understanding of particles and particle behavior based upon statistical probabilities. Although some philosophers and metaphysicists would like to keep the hidden variable argument alive, the experimental evidence is persuasive, compelling, and conclusive that such hidden variables do not exist.

See also Quantum number.