Equation de Schrödinger

Valores del function de unda

Le function $\psi (𝐱,t)=<𝐱|\psi (t)>=<𝐱|e^{-\frac{i}{\hslash }\mathscr{H}t}|\psi >$ obedi le equation de Schrödinger

$H\psi (𝐱,t)=-\frac{{\hslash }^2}{2m}\mathrm{\nabla }\psi (𝐱,t)+U(𝐱,t)\psi (𝐱,t)=i\hslash \frac{\partial }{\partial t}\psi (𝐱,t)$

ubi $U(𝐱,t)$ es un energia potential. H es le operator de energia (le function de Hamilton) o operator Hamiltoniano

$H=\frac{p^2}{2m}+U=-\frac{{\hslash }^2}{2m}\mathrm{\nabla }+U(𝐱,t).$

Le decomposition

$\psi (𝐱,t)=\sum _n{c}_n(t){\psi }_n(𝐱)$

transforma le equation temporal de Schrödinger in le

$H{\psi }_n(𝐱,t)=E_n{\psi }_n(𝐱,t)$

equation non temporal de Schrödinger, con $c_n(t)=e^{-i\frac{E_{n}t}{\hslash }}.$

Vide etiam

• Mechanica quantic