A wave function or wavefunction is a probability amplitude in quantum mechanics describing the quantum state of a particle and how it behaves. Typically, its values are complex numbers and, for a single particle, it is a function of space and time. The laws of quantum mechanics (the Schrödinger equation) describe how the wave function evolves over time. The wave function behaves qualitatively like other waves, like 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.
The most common symbols for a wave function are ψ or Ψ (lower-case and capital psi).
Although ψ is a complex number, |ψ|2 is real, and corresponds to the probability density of finding a particle in a given place at a given time, if the particle's position is measured.
The SI units for ψ depend on the system. For one particle in three dimensions, its units are m–3/2. These unusual units are required so that an integral of |ψ|2 over a region of three-dimensional space is a unitless probability (i.e., the probability that the particle is in that region). For different numbers of particles and/or dimensions, the units may be different (but they can be determined by dimensional analysis).
The wave function is central to quantum mechanics, because it is a fundamental postulate of quantum mechanics. It is the source of the mysterious consequences and philosophical difficulties in the interpretations of quantum mechanics—topics that continue to be debated even today.
Other articles related to "wave functions, wave function, wave, function":
... to remove or minimize spin contamination from UHF wave functions have been proposed ... The resulting wave function, while not completely free of contamination, dramatically improves upon the UHF approach especially in the absence of high order contamination ... Projected UHF (PUHF) annihilates all spin contaminants from the self-consistent UHF wave function ...
... coordinates on the 1 dimensional semicircle, the wave function depends only on the angular coordinate, and so Substituting the Laplacian in ... The wave function can now be expressed as, which is easily solvable ... the boundary conditions, where and are continuous and the wave function is normalizable ...
... Within Hartree–Fock theory, the wave function is approximated as a Slater determinant of spin-orbitals ... In general, an N-electron Hartree–Fock wave function composed of Nα α-spin orbitals and Nβ β-spin orbitals can be written as where is the antisymmetrization operator ... This wave function is an eigenfunction of the total spin projection operator, Ŝz, with eigenvalue (Nα − Nβ)/2 (assuming Nα ≥ Nβ) ...
... The multislice algorithm is an approach to solving the Schrödinger wave equation The following section will include a mathematical formulation of the Multislice algorithm ... in the form of incident and scattered wave as where is the Green’s function that represents the amplitude of the electron wave function at a point due to a source at point ... Hence for an incident plane wave of the form the Schrödinger equation can be written as We then choose the coordinate axis in such a way that the incident beam hits the sample at (0,0,0) in the -dire ...
Famous quotes containing the words function and/or wave:
“Morality and its victim, the motherwhat a terrible picture! Is there indeed anything more terrible, more criminal, than our glorified sacred function of motherhood?”
—Emma Goldman (18691940)
“I dont know a great deal about life in Washington for womenI spent a summer there once working in the White House, and my main memories of the experience have to do with a very bad permanent wave I have always been convinced kept me from having a meaningful relationship with President Kennedy ...”
—Nora Ephron (b. 1941)