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.../math> transforms to <math>|\bar{\psi}\rangle=U|\psi\rangle.</math> The [[Schrödinger equation]] must still hold in this new picture, so

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 coupled

...uantum mechanics]] where the central equation&mdash;the time-independent [[Schrödinger equation]]&mdash;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 appropriateness

...]] 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''&mdash;for benzene an equation in 36 variable

...the motion of very light material particles, such as [[electron]]s. When [[Schrödinger equation|Schrödinger's wave equation]] is solved with appropriate boundary conditio

...the wave nature of matter. In 1926, [[Erwin Schrödinger]]'s (1887-1961) [[Schrödinger equation|wave equation]] described the behaviour of electrons and other particles em

...anics]], the energy levels of a system can be determined by solving the [[Schrödinger equation]] ''H'' &Psi; = E &Psi;, This operator appears also in the (&theta;, &phi;)-part of the Schrödinger equation of the [[hydrogen-like atom]]s,

...). This is important in [[quantum mechanics]], since the one-dimensional [[Schrödinger equation]] is a special case of a S–L equation.

...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 [[micr

...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 th

...the basic laws of quantum mechanics, but here we consider just one: the [[Schrödinger equation]], discovered by Erwin Schrödinger in 1926. In rectangular coordinates, it

...]'s equation ''F=ma'', [[Einstein]]'s equation ''E=mc²'', and [[Schrödinger equation|Schrödinger]]'s equation ''H&psi;=E&psi;''. Yet, among the general, well-e

...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/>

...functions show the symmetry of the system. [Technically: solutions of the Schrödinger equation belong to a subspace of Hilbert (function) space that is irreducible unde

...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 [[Oper

...lar Hamiltonian]] (quantum mechanical energy operator). Solutions of the Schrödinger equation (wave functions) open the door to all kinds of molecular properties of chem

...rbation theory one assumes that the unperturbed (without external field) [[Schrödinger equation]]s are solved

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...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.

Solutions of the Schrödinger equation for the hydrogen atom gives the form of the wave function for [[atomic orbi