- Person
- Eugene Wigner
- Lived
- 1902–1995
- Field
- Theoretical physics
- From
- Hungarian-American
The story
Crystals are built from atoms arranged in a regular three-dimensional pattern called a lattice. The properties of crystalline materials stem from this highly ordered structure. To study such a periodic system, physicists need a convenient way to describe its symmetry and the region of space that belongs to each lattice point. Eugene Wigner had entered physics through crystallography in 1926, when he helped the crystallographer Karl Weissenberg understand why atoms sit at symmetric positions in crystals.
At Princeton in the early 1930s Wigner supervised the doctorate of Frederick Seitz. In a 1933 paper the two proposed applying a geometric construction to the physics of solids: they used it to solve the Schrödinger equation for the free electrons in metallic sodium. In sodium the cell is a truncated octahedron, which they approximated as a sphere of the same volume, allowing them to solve the equation exactly. John C. Slater later carried out a similar calculation that took the true shape into account.
The construction is now called the Wigner–Seitz cell. Around a chosen lattice point, it is the region of space closer to that point than to any other lattice point. It can be drawn by connecting the point to its neighbours and drawing a perpendicular plane through the midpoint of each line; the smallest region enclosed is the cell. It is a primitive cell, containing exactly one lattice point, and although any lattice has infinitely many possible primitive cells, it has only one Wigner–Seitz cell. Mathematically it is an example of a Voronoi cell, an idea earlier studied by Dirichlet, Fedorov and Voronoy.
The same construction applied to the reciprocal lattice in momentum space gives the Brillouin zone, a central concept in the theory of how electrons and vibrations move through solids. Seitz went on to become a leading figure in solid-state physics, and the Wigner–Seitz method was one of the early steps in calculating the electronic structure of real metals.
The Wigner–Seitz cell is widely taught to students of crystallography and solid-state physics. It remains a natural way to describe the space belonging to each lattice point in a crystal, and a basic tool in the physics of solids, the field that underpins modern electronics.
Why it matters
The Wigner–Seitz construction is a basic tool in the physics of solids, which underpins semiconductors and much of modern electronics.
About Eugene Wigner
Budapest-born Nobel physicist who brought symmetry and group theory into quantum mechanics, helped launch the Manhattan Project and designed the first plutonium production reactors.
More about Eugene Wigner
- Eugene Wigner brought group theory into quantum physicsEugene Wigner's 1931 book Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra made the mathematics of symmetry usable by a generation of physicists.
- Eugene Wigner introduced the concept of parityIn his 1927 paper On the Conservation Laws of Quantum Mechanics, Eugene Wigner introduced parity, the mirror symmetry of quantum systems, now a basic idea in physics.
- Eugene Wigner's 1932 function links quantum and classicalIn 1932 Eugene Wigner introduced the Wigner function, a way of picturing quantum states in classical-style phase space now used in quantum optics, chemistry and signal processing.
- Wigner asked why mathematics describes nature so wellEugene Wigner's 1960 essay The Unreasonable Effectiveness of Mathematics in the Natural Sciences asked why abstract mathematics fits the physical world so astonishingly well.
Sources
- Wigner–Seitz cell Wikipedia
- Eugene Wigner Wikipedia
- Eugene Paul Wigner MacTutor History of Mathematics, University of St Andrews
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