- Person
- Eugene Wigner
- Lived
- 1902–1995
- Field
- Theoretical physics
- From
- Hungarian-American
The story
In classical physics a particle has a definite position and momentum, so it can be pictured as a point in "phase space", and a collection of particles can be described by a probability distribution over that space. Quantum mechanics does not allow this. The uncertainty principle forbids knowing position and momentum exactly at the same time, and quantum states are described instead by wavefunctions, which look very different from the classical picture.
In 1932 Eugene Wigner, then dividing his time between Princeton and Berlin, looked for a bridge between the two descriptions. To study quantum corrections to classical statistical mechanics, he introduced what is now called the Wigner quasiprobability distribution, or Wigner function. Its goal was to link the wavefunction of the Schrödinger equation to a distribution over position and momentum. It is closely related to a correspondence between phase-space functions and quantum operators introduced by Hermann Weyl in 1927, and it is also known as the Wigner–Ville distribution, after Wigner and Jean-André Ville.
The Wigner function behaves much like a classical probability distribution, with one striking difference: it can take negative values. For states that have no classical counterpart it normally does, which makes it a convenient indicator of quantum interference. The negative regions are always small, no larger than a few units of Planck's constant, so they are shielded by the uncertainty principle and disappear in the classical limit. Smoothing the function slightly produces a positive distribution that can be read in a more classical way.
The function has applications in statistical mechanics, quantum chemistry, quantum optics and classical optics. Through the related Wigner distribution function in signal processing, it is also used in electrical engineering, seismology, the time-frequency analysis of music, spectrograms in biology, speech processing and even engine design, wherever engineers need to see how a signal's frequencies change over time.
Few ideas travel so far from their origin. A tool devised to study quantum corrections to statistical mechanics has become a standard way to picture quantum states of light and matter, and its negative regions serve as a convenient signature of genuinely quantum behaviour.
Why it matters
The Wigner function is a standard tool for studying quantum light and quantum technologies, and its offshoots help engineers analyse complex signals.
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.
- The Wigner–Seitz cell helps map crystalsWith his student Frederick Seitz, Eugene Wigner gave his name to the Wigner–Seitz cell, a standard way of dividing up a crystal lattice used throughout solid-state physics.
- 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 quasiprobability distribution Wikipedia
- Eugene Wigner Wikipedia
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