Wiktionary
n. (alternative spelling of wavefunction English)
Wikipedia
The classical process (A–B) is represented as the motion of a particle along a trajectory. The quantum process (C–H) has no such trajectory. Rather, it is represented as a wave. Panels (C–F) show four different standing wave solutions of the Schrödinger equation. Panels (G–H) further show two different wave functions that are solutions of the Schrödinger equation but not standing waves.]]
A wave function in quantum mechanics is a description of the quantum state of a system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements made on the system can be derived from it. The most common symbols for a wave function are the Greek letters or (lower-case and capital psi).
The wave function is a function of the degrees of freedom corresponding to some maximal set of commuting observables. Once such a representation is chosen, the wave function can be derived from the quantum state.
For a given system, the choice of which commuting degrees of freedom to use is not unique, and correspondingly the domain of the wave function is not unique. For instance it may be taken to be a function of all the position coordinates of the particles over position space, or the momenta of all the particles over momentum space, the two are related by a Fourier transform. Some particles, like electrons and photons, have nonzero spin, and the wave function for such particles includes spin as an intrinsic, discrete degree of freedom. Other discrete variables can also be included, such as isospin. When a system has internal degrees of freedom, the wave function at each point in the continuous degrees of freedom (e.g. a point in space) assigns a complex number for each possible value of the discrete degrees of freedom (e.g. z-component of spin). These values are often displayed in a column matrix (e.g. a column vector for a non-relativistic electron with spin ).
According to the superposition principle of quantum mechanics, wave functions can be added together and multiplied by complex numbers to form new wave functions and form a Hilbert space. The inner product between two wave functions is a measure of the overlap between the corresponding physical states and is used in the foundational probabilistic interpretation of quantum mechanics, the Born rule, relating transition probabilities to inner products. The Schrödinger equation determines how wave functions evolve over time. A wave function behaves qualitatively like other waves, such as water waves or waves on a string, because the Schrödinger equation is mathematically a type of wave equation. This explains the name "wave function", and gives rise to wave–particle duality. However, the wave function in quantum mechanics describes a kind of physical phenomenon, still open to different interpretations, which fundamentally differs from that of classic mechanical waves.
In Born's statistical interpretation in non-relativistic quantum mechanics, the squared modulus of the wave function, , is a real number interpreted as the probability density of measuring a particle's being detected at a given place, or having a given momentum, at a given time, and possibly having definite values for discrete degrees of freedom. The integral of this quantity, over all the system's degrees of freedom, must be 1 in accordance with the probability interpretation, this general requirement a wave function must satisfy is called the normalization condition. Since the wave function is complex valued, only its relative phase and relative magnitude can be measured. Its value does not in isolation tell anything about the magnitudes or directions of measurable observables; one has to apply quantum operators, whose eigenvalues correspond to sets of possible results of measurements, to the wave function and calculate the statistical distributions for measurable quantities.
Usage examples of "wave function".
The collapse of the wave function is an example of transcription (after all, the electron manifests as an electron and not a frog).
A scrolling graph of brain-wave function showed him to still be in a state of narcotized sleep, though with abnormal spikes of activity throughout the thalamocortical zones.
A framed photograph of Hunt with a couple of grinning colleagues and a group of Ganymeans posing in front of a backdrop of the Shapieron was propped on top of the frame of a four-foot wallscreen showing a contour plot of some kind of three-dimensional wave function.
An equation lay there, a collapsing wave function, unsolvable using present-day mathematics.
Not even the world's most powerful supercomputers could solve a collapsing wave function.
But the machine that could solve a collapsing wave function would be capable of a lot more than computing.
That, too, is a sum of all possibilities - using the universe's quantum wave function in place of the light intensity due to the photon - so by the same token, we can interpret the mathematics in a similarly dramatic way.
Where the wave function has its peaks is where I'm most likely to find my electron&mdash.
That reality - the Universe itself - was called into existence by conscious minds, as, by observation, they collapsed the infinite possibilities of each quantum wave function into a single, definite event, embedded in history.