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diff --git a/vorlesungen/slides/2/hilbertraum/energie.tex b/vorlesungen/slides/2/hilbertraum/energie.tex new file mode 100644 index 0000000..7868cb4 --- /dev/null +++ b/vorlesungen/slides/2/hilbertraum/energie.tex @@ -0,0 +1,62 @@ +% +% energie.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Energie --- Zeitentwicklung --- Schrödinger} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.30\textwidth} +\begin{block}{Totale Energie} +Hamilton-Funktion +\begin{align*} +H +&= +\frac12mv^2 + V(x) +\\ +&= +\frac{p^2}{2m} + V(x) +\end{align*} +\end{block} +\begin{block}{Quantisierungsregel} +\begin{align*} +\text{Variable}&\to \text{Operator} +\\ +x_k & \to x_k +\\ +p_k & \to \frac{\hbar}{i} \frac{\partial}{\partial x_k} +\end{align*} +\end{block} +\end{column} +\begin{column}{0.66\textwidth} +\begin{block}{Energie-Operator} +\[ +H += +-\frac{\hbar^2}{2m}\Delta + V(x) +\] +\end{block} +\begin{block}{Eigenwertgleichung} +\[ +-\frac{\hbar^2}{2m}\Delta\psi(x,t) + V(x)\psi(x,t) = E\psi(x,t) +\] +Zeitunabhängige Schrödingergleichung +\end{block} +\begin{block}{Zeitabhängigkeit = Schrödingergleichung} +\[ +-\frac{\hbar}{i} +\frac{\partial}{\partial t} +\psi(x,t) += +-\frac{\hbar^2}{2m}\Delta\psi(x,t) + V(x)\psi(x,t) +\] +Eigenwertgleichung durch Separation von $t$ +\end{block} +\end{column} +\end{columns} +\end{frame} +\egroup |