# Wave Functions

### Some articles on wave, function, wave function, wave functions, functions, waves:

Dihydrogen Cation - Quantum Mechanical Treatment, Symmetries, and Asymptotics
... The simplest electronic Schrödinger wave equation for the hydrogen molecular ion is modeled with two fixed nuclear centers, labeled A and B, and one electron ... It can be written as where is the electron-nuclear Coulomb potential energy function and E is the (electronic) energy of a given quantum mechanical state (eigenstate), with the ... In atomic units the wave equation is We can choose the midpoint between the nuclei as the origin of coordinates ...
Aharonov–Bohm Effect - Mathematical Interpretation
... effect can be understood from the fact that we can only measure absolute values of the wave function ... operator with zero momentum to be the function "1" (ignoring normalization problems) and specifying wave functions relative to this eigenfunction "1" ... This means that it is physically more natural to describe wave "functions", in the language of differential geometry, as sections in a complex line bundle ...
Helium Atom - Hartree-Fock Method
... Schrödinger equation for the spatial part of the two-electron wave function will reduce to the 'zero-order' equation This equation is separable and the eigenfunctions can be written in ... The exact spatial wave functions of two-electron atoms must either be symmetric or antisymmetric with respect to the interchange of the coordinates and of the two electrons ... The proper wave function then must be composed of the symmetric (+) and antisymmetric(-) linear combinations The factor normalizes ...
Muffin-tin Approximation
... Augmented plane wave method is a method which uses muffin tin approximation ... Wave functions (the augmented plane waves) are constructed by matching solutions of the Schrödinger equation within each sphere with plane-wave solutions in the interstitial region, and linear combinations of ... Among them are the augmented plane wave (APW) method, the linear muffin-tin orbital method (LMTO) and various Green's function methods ...
Scanning Tunneling Microscope - Principle of Operation
... If an electron of energy E is incident upon an energy barrier of height U(z), the electron wave function is a traveling wave solution, where if E > U(z), which is true for a wave ... Inside a barrier, E < U(z) so the wave functions which satisfy this are decaying waves, where quantifies the decay of the wave inside the barrier, with the barrier in the +z ... Quantum oscillations Scanning tunneling microscopy Knowing the wave function allows one to calculate the probability density for that electron to be ...

### Famous quotes containing the words functions and/or wave:

Empirical science is apt to cloud the sight, and, by the very knowledge of functions and processes, to bereave the student of the manly contemplation of the whole.
Ralph Waldo Emerson (1803–1882)

Wind goes from farm to farm in wave on wave,
But carries no cry of what is hoped to be.
There may be little or much beyond the grave,
But the strong are saying nothing until they see.
Robert Frost (1874–1963)