Equation de Schrödinger

Valores del function de unda

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

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

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

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

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

Le decomposition

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

transforma le equation temporal de Schrödinger in le

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

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

Vide etiam

• Mechanica quantic