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{{r|Schrödinger equation}}

{{r|Schrödinger equation}}

{{r|Schrödinger equation}}

{{r|Schrödinger equation}}

...tor is one of the few systems that can be treated exactly, ''i.e.'', its [[Schrödinger equation]] can be solved analytically. ...ly referred to as the "bottom of the potential well". As stated above, the Schrödinger equation of the one-dimensional quantum harmonic oscillator can be solved exactly, y

{{r|Schrödinger equation}}

...are [[Newton's laws]], the equation of a [[harmonic oscillator]] and the [[Schrödinger equation]].

{{r|Schrödinger equation}}

...uation in early 1926. Actually there are two different equations known as Schrödinger equation: The first is sometimes called the time-dependent, while the second is call Mathematically, the time-independent Schrödinger equation is an example of an [[eigenvalue problem]] whose eigenvectors ψ are ca

{{r|Schrödinger equation}}

...theory of the hydrogen atom, but it is also part of the solution of the [[Schrödinger equation]] for [[hydrogen-like atom]]s. It is a positive integer (''n'' = 1, 2, 3, & ..., ''ℓ'' runs from 0 to ''n''−1, as follows from the solution of the Schrödinger equation. In total, an atomic shell with quantum number ''n'' consists of ''n'' sub

...problems go back to the earliest days, but until the formulation of the [[Schrödinger equation]] by the [[Austria]]n [[physics|physicist]] [[Erwin Schrödinger]], the tec

..., the effective Schrödinger equation is invariant under rotation, like the Schrödinger equation of the one-electron atoms, it can be shown that the angular parts of the so ...ns (briefly orbitals) are needed in many numerical methods for solving the Schrödinger equation of atoms and molecules. Functions of ''r''_A1 (the distance of el

...ne]</ref> This was the same year that [[Erwin Schrödinger]] proposed his [[Schrödinger equation|wave equation]], which formed the basis of the new [[quantum mechanics]]. I

...e square well''' problem is one of the simplest non-trivial solutions to [[Schrödinger equation|Schrödinger's wave equation]]. As such it is often encountered in introdu ...ial does not depend on time we can use the time-independent version of the Schrödinger equation. With <math>V(x)=0</math> in the box the [[wavefunction]], <math>\psi(x)</

The 3D time-independent Schrödinger equation for this system is We can now cancel <math>\psi</math> from both sides of Schrödinger equation above, giving us

...first step in solving a quantum chemical problem is usually solving the [[Schrödinger equation]] (or [[Dirac equation]] in [[relativistic quantum chemistry]]) with the [[ ...tonian]] in order to study the motion of molecules. Direct solution of the Schrödinger equation is called ''quantum molecular dynamics'', within the [[semiclassical]] appr

...''m'' (this is the [[reduced mass]] of the two charged particles) and the Schrödinger equation becomes, ===Schrödinger equation of dimer===

...only on the distance between the two particles, their non-relativistic [[Schrödinger equation]] can be solved in analytic form. The solutions are one-electron functions ...dinger equation can be solved analytically, in exactly the same way as the Schrödinger equation of the hydrogen atom.

...g that an orbital is seen as a solution of an (effective) ''one-electron [[Schrödinger equation]]''. This point of view is a narrowing of the more general quantum chemical see the section ''solution of the atomic Schrödinger equation'' in [[atomic orbital]] for more on this. Very often atomic orbitals are d