Equation de Schrödinger

Valores del function de unda

Equation de Schrödinger
subclasse de: partial differential equation[*]
Commons: Schrödinger equation

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

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

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

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

Le decomposition

$\psi (\mathbf {x} ,t)=\sum _{n}c_{n}(t)\psi _{n}(\mathbf {x} )$

transforma le equation temporal de Schrödinger in le

$H\psi _{n}(\mathbf {x} ,t)=E_{n}\psi _{n}(\mathbf {x} ,t)$

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

Vide etiam

• Mechanica quantic