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- ...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 ca17 KB (2,678 words) - 10:12, 9 May 2011
- 2 KB (197 words) - 09:40, 28 March 2011
- 145 bytes (18 words) - 16:32, 23 May 2008
- 12 bytes (1 word) - 14:02, 14 November 2007
- Auto-populated based on [[Special:WhatLinksHere/Schrödinger equation]]. Needs checking by a human.1 KB (143 words) - 10:13, 9 May 2011
- 167 bytes (23 words) - 18:10, 26 March 2011
Page text matches
- {{r|Schrödinger equation||**}}659 bytes (72 words) - 10:05, 12 June 2009
- #REDIRECT [[Schrödinger equation]]35 bytes (4 words) - 09:33, 26 March 2011
- #REDIRECT[[Schrödinger equation]]34 bytes (4 words) - 02:23, 18 February 2007
- {{R|Schrödinger equation}}572 bytes (67 words) - 07:18, 2 October 2008
- {{r|Schrödinger equation}}207 bytes (24 words) - 18:14, 26 August 2009
- The [[Schrödinger equation]] is a partial differential equation (or PDE) of fundamental importance in ...ial differential equation]]s is that the unknown (<math>\psi</math> in the Schrödinger equation, and u in the heat equation) depends on multiple variables, and the equatio4 KB (657 words) - 16:03, 6 May 2010
- * {{r|Schrödinger equation}}122 bytes (14 words) - 07:07, 22 June 2008
- *[[Theoretical and experimental justification for the Schrödinger equation]]473 bytes (45 words) - 14:05, 26 September 2010
- This means that in the case of one spatial dimension [[Schrödinger equation|Schrödinger's equation]] is given everywhere by4 KB (711 words) - 09:31, 26 March 2011
- Auto-populated based on [[Special:WhatLinksHere/Schrödinger equation]]. Needs checking by a human.1 KB (143 words) - 10:13, 9 May 2011
- *the wavefunction ψ (the solution to the [[Schrödinger equation]]) is a complete description of a system *the wavefunction evolves in time according to the time-dependent Schrödinger equation4 KB (558 words) - 12:26, 9 May 2011
- {{r|Schrödinger equation}}476 bytes (61 words) - 20:07, 11 January 2010
- {{r|Schrödinger equation}}550 bytes (65 words) - 14:24, 19 October 2010
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- {{r|Schrödinger equation}}678 bytes (85 words) - 18:36, 11 January 2010
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- {{r|Schrödinger equation}}748 bytes (97 words) - 20:03, 11 January 2010
- {{r|Schrödinger equation}}704 bytes (87 words) - 17:05, 11 January 2010
- {{r|Schrödinger equation}}635 bytes (85 words) - 09:22, 26 March 2011
- ...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, y10 KB (1,632 words) - 21:28, 11 September 2021
- {{r|Schrödinger equation}}936 bytes (115 words) - 12:57, 15 March 2024
- ...are [[Newton's laws]], the equation of a [[harmonic oscillator]] and the [[Schrödinger equation]].6 KB (951 words) - 05:01, 8 December 2009
- {{r|Schrödinger equation}}1 KB (173 words) - 05:43, 6 March 2024
- ...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 ca17 KB (2,678 words) - 10:12, 9 May 2011
- {{r|Schrödinger equation}}2 KB (229 words) - 09:18, 6 March 2024
- ...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'' sub5 KB (873 words) - 15:11, 15 May 2022
- ...problems go back to the earliest days, but until the formulation of the [[Schrödinger equation]] by the [[Austria]]n [[physics|physicist]] [[Erwin Schrödinger]], the tec4 KB (592 words) - 03:37, 15 November 2007
- ..., 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''<sub>A1</sub> (the distance of el14 KB (2,265 words) - 05:37, 6 March 2024
- ...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]]. I4 KB (577 words) - 13:21, 3 November 2021
- ...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)</16 KB (2,810 words) - 11:31, 5 April 2011
- 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 us8 KB (1,340 words) - 07:25, 27 October 2007
- ...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]] appr9 KB (1,219 words) - 14:19, 19 October 2010
- ...''m'' (this is the [[reduced mass]] of the two charged particles) and the Schrödinger equation becomes, ===Schrödinger equation of dimer===15 KB (2,231 words) - 00:49, 21 October 2013
- ...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.19 KB (2,981 words) - 18:31, 3 November 2021
- ...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 d10 KB (1,514 words) - 19:38, 20 November 2009
- .../math> transforms to <math>|\bar{\psi}\rangle=U|\psi\rangle.</math> The [[Schrödinger equation]] must still hold in this new picture, so10 KB (1,685 words) - 12:22, 14 November 2007
- In [[quantum chemistry]], the solution of a set of coupled nuclear motion [[Schrödinger equation]]s can be eased by a '''diabatic transformation'''. Such a set of coupled13 KB (1,922 words) - 07:19, 7 May 2010
- ...uantum mechanics]] where the central equation—the time-independent [[Schrödinger equation]]—has the form of an eigenvalue equation of an operator commonly den ...ion of the operator eigenvalue equation to be solved (the time-independent Schrödinger equation). The success of the method relies to a large extent on the appropriateness12 KB (1,893 words) - 04:51, 25 March 2010
- ...]] molecule consists of 12 nuclei and 42 electrons. The [[time-independent Schrödinger equation]], which must be solved to obtain the energy and molecular wave function of ...cond step of the BO approximation this function serves as a potential in a Schrödinger equation ''containing only the nuclei''—for benzene an equation in 36 variable20 KB (3,194 words) - 03:34, 8 November 2013
- ...the motion of very light material particles, such as [[electron]]s. When [[Schrödinger equation|Schrödinger's wave equation]] is solved with appropriate boundary conditio13 KB (1,900 words) - 10:49, 30 November 2009
- ...the wave nature of matter. In 1926, [[Erwin Schrödinger]]'s (1887-1961) [[Schrödinger equation|wave equation]] described the behaviour of electrons and other particles em7 KB (963 words) - 03:55, 1 November 2010
- ...anics]], the energy levels of a system can be determined by solving the [[Schrödinger equation]] ''H'' Ψ = E Ψ, This operator appears also in the (θ, φ)-part of the Schrödinger equation of the [[hydrogen-like atom]]s,25 KB (3,876 words) - 03:13, 1 October 2013
- ...). This is important in [[quantum mechanics]], since the one-dimensional [[Schrödinger equation]] is a special case of a S–L equation.15 KB (2,332 words) - 04:52, 18 October 2009
- ...rovibrational) Schrödinger equation of a [[molecule]]. The rovibrational Schrödinger equation arises in the second step of the [[Born-Oppenheimer approximation]] (BO ap ...O approximation. The eigenvalues obtained from the solution of the nuclear Schrödinger equation are the energies observed in the [[infrared spectrum|infrared]] and [[micr20 KB (3,213 words) - 02:14, 23 February 2010
- ...lecular Hamiltonian, (i.e., by solution of the associated time-independent Schrödinger equation). Properties that can be computed are first and foremost (reaction) energie ...n the full Coulomb Hamiltonian are very rare. The main reason is that its Schrödinger equation is almost impossible to solve, even approximately. Applications based on th31 KB (4,757 words) - 02:20, 27 October 2013
- ...the basic laws of quantum mechanics, but here we consider just one: the [[Schrödinger equation]], discovered by Erwin Schrödinger in 1926. In rectangular coordinates, it20 KB (3,304 words) - 17:11, 25 August 2013
- ...]'s equation ''F=ma'', [[Einstein]]'s equation ''E=mc<sup>2</sup>'', and [[Schrödinger equation|Schrödinger]]'s equation ''Hψ=Eψ''. Yet, among the general, well-e18 KB (2,680 words) - 18:46, 16 December 2010
- ...mechanics]], the ''envelope approximation'' usually is used in which the [[Schrödinger equation]] is simplified to refer only to the behavior of the envelope, and boundary where the coefficients ''A''('''''k''''') are found from the approximate Schrödinger equation, and ''V'' is the crystal volume.<ref name=impurity/>12 KB (1,810 words) - 11:41, 18 June 2012
- ...functions show the symmetry of the system. [Technically: solutions of the Schrödinger equation belong to a subspace of Hilbert (function) space that is irreducible unde8 KB (1,408 words) - 09:47, 24 April 2010
- ...ime, a role similar to [[Newton's second law]] in classical mechanics. The Schrödinger equation, applied to our free particle, predicts that the center of a wave packet wi The time evolution of a quantum state is described by the [[Schrödinger equation]], in which the [[Hamiltonian (quantum mechanics)|Hamiltonian]], the [[Oper37 KB (5,578 words) - 04:54, 21 March 2024
- ...lar Hamiltonian]] (quantum mechanical energy operator). Solutions of the Schrödinger equation (wave functions) open the door to all kinds of molecular properties of chem20 KB (3,082 words) - 17:39, 9 December 2008
- ...rbation theory one assumes that the unperturbed (without external field) [[Schrödinger equation]]s are solved12 KB (1,839 words) - 10:43, 5 October 2009
- <!--time-independent Schrödinger equation -->7 KB (1,257 words) - 03:23, 24 March 2010
- ...been switched on, angular momentum coupling will be useful in solving the Schrödinger equation of the total system. ...g the eigenvectors of ''H'', i.e., in the solution of the time-independent Schrödinger equation of the example two-electron atom.21 KB (3,338 words) - 10:45, 11 June 2009
- Solutions of the Schrödinger equation for the hydrogen atom gives the form of the wave function for [[atomic orbi22 KB (3,143 words) - 09:41, 6 March 2024
- Solutions of the Schrödinger equation for the hydrogen atom gives the form of the wave function for [[atomic orbi23 KB (3,309 words) - 09:41, 6 March 2024
- ...agrange]], or [[Hamilton]], or the equation may be the quantum mechanical Schrödinger equation. The choice depends on whether or not quantum effects are important for the56 KB (8,720 words) - 07:31, 20 April 2024
- which is the time-''in''dependent [[Schrödinger equation]]. By using ''n'' to label the [[eigenstates]] ψ<sub>''n''</sub>, we ma43 KB (7,032 words) - 15:15, 15 August 2022
- ...ysical or mathematical prerequisites are needed. Nothing like Newton laws, Schrödinger equation, conservation laws, nor even particles or waves. Nothing like differentiati24 KB (3,745 words) - 02:21, 26 October 2013
- ...known atomic orbitals are those of [[hydrogen-like atom]]s for which the [[Schrödinger equation]] can be solved exactly. Hybridised orbitals are assumed to be mixtures of14 KB (2,154 words) - 09:32, 12 November 2007
- ...ert in behavior. (See the article [[Atomic orbital#Solutions of the atomic Schrödinger equation|atomic orbital]] for a more detailed explanation of the building up of the13 KB (2,075 words) - 09:16, 6 March 2024
- If one solves the Schrödinger equation with total Hamiltonian ''H'' = ''H''<sub>0</sub> + ''V'' one obtains a tot17 KB (2,690 words) - 01:15, 22 September 2009
- ...The symbol "''d''" stands for an [[Atomic orbital#Solutions of the atomic Schrödinger equation|atomic orbital]] with [[angular momentum (quantum)|angular momentum]] quant22 KB (3,166 words) - 06:33, 6 March 2024
- ...e ground and excited states of the H-atom are known exactly, because the [[Schrödinger equation]] can be solved analytically for one-electron atoms, see [[hydrogen-like at20 KB (3,081 words) - 21:57, 31 March 2022