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Valores del function de unda
Le function
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)}](http://178.128.105.246/content-https-wikimedia.org/api/rest_v1/media/math/render/svg/d1020ac1d08d4a531a446de61b8f61a3d6869be2)
ubi
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).}](http://178.128.105.246/content-https-wikimedia.org/api/rest_v1/media/math/render/svg/445ab3902ae404229f49e02acfc746b796e1345a)
Le decomposition
![{\displaystyle \psi (\mathbf {x} ,t)=\sum _{n}c_{n}(t)\psi _{n}(\mathbf {x} )}](http://178.128.105.246/content-https-wikimedia.org/api/rest_v1/media/math/render/svg/4d996185e8a03c3dbf2c321c707ab8c73852b294)
transforma le equation temporal de Schrödinger in le
![{\displaystyle H\psi _{n}(\mathbf {x} ,t)=E_{n}\psi _{n}(\mathbf {x} ,t)}](http://178.128.105.246/content-https-wikimedia.org/api/rest_v1/media/math/render/svg/637b57c706bf96611b335c4d65fa4c41504af92c)
equation non temporal de Schrödinger, con