Χρήστης:Mike.ip1993/πρόχειρο: Διαφορά μεταξύ των αναθεωρήσεων

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Αντικατάσταση παρωχημένης σύνταξης latex (mw:Extension:Math/Roadmap)
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μ (Αντικατάσταση παρωχημένης σύνταξης latex (mw:Extension:Math/Roadmap))
 
This equation is formally similar to the particle diffusion equation, which one obtains through the following transformation:
:<math>\begin{align}
c(\boldmathbf R,t) &\to \psi(\boldmathbf R,t) \\
D &\to \frac{i \hbar}{2m}
\end{align}</math>
Applying this transformation to the expressions of the Green functions determined in the case of particle diffusion yields the Green functions of the [[Schrödinger equation]], which in turn can be used to obtain the [[wave function]] at any time through an integral on the [[wave function]] at ''t'' = 0:
: <math>\psi(\boldmathbf R, t) = \int \psi(\boldmathbf R^0,t=0) G(\boldmathbf R - \boldmathbf R^0,t) dR_x^0\,dR_y^0\,dR_z^0,</math>
with
:<math>G(\boldmathbf R,t) = \bigg( \frac{m}{2 \pi i \hbar t} \bigg)^{3/2} e^{-\frac {\boldmathbf R^2 m}{2 i \hbar t}}.</math>
 
Remark: this analogy between quantum mechanics and diffusion is a purely formal one. Physically, the evolution of the [[wave function]] satisfying [[Schrödinger's equation]] might have an origin other than diffusion.
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