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author | Lukaszogg <82384106+Lukaszogg@users.noreply.github.com> | 2021-07-08 20:10:11 +0200 |
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committer | Lukaszogg <82384106+Lukaszogg@users.noreply.github.com> | 2021-07-08 20:10:11 +0200 |
commit | 14033ca595b5c933caea3b214d2246529e6845b8 (patch) | |
tree | 0d6d2b2eb34e5ef5df3c517be5c1c9d803fa066c /vorlesungen/slides/2/hilbertraum/energie.tex | |
parent | Update teil1.tex (diff) | |
parent | Only include buch.ind if it exists. (diff) | |
download | SeminarMatrizen-14033ca595b5c933caea3b214d2246529e6845b8.tar.gz SeminarMatrizen-14033ca595b5c933caea3b214d2246529e6845b8.zip |
Merge remote-tracking branch 'upstream/master'
Diffstat (limited to 'vorlesungen/slides/2/hilbertraum/energie.tex')
-rw-r--r-- | vorlesungen/slides/2/hilbertraum/energie.tex | 67 |
1 files changed, 67 insertions, 0 deletions
diff --git a/vorlesungen/slides/2/hilbertraum/energie.tex b/vorlesungen/slides/2/hilbertraum/energie.tex new file mode 100644 index 0000000..202a7c5 --- /dev/null +++ b/vorlesungen/slides/2/hilbertraum/energie.tex @@ -0,0 +1,67 @@ +% +% 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} +\uncover<2->{% +\begin{block}{Totale Energie} +Hamilton-Funktion +\begin{align*} +H +&= +\frac12mv^2 + V(x) +\\ +&= +\frac{p^2}{2m} + V(x) +\end{align*} +\end{block}} +\uncover<3->{% +\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} +\uncover<4->{% +\begin{block}{Energie-Operator} +\[ +H += +-\frac{\hbar^2}{2m}\Delta + V(x) +\] +\end{block}} +\uncover<5->{% +\begin{block}{Eigenwertgleichung} +\[ +-\frac{\hbar^2}{2m}\Delta\psi(x,t) + V(x)\psi(x,t) = E\psi(x,t) +\] +Zeitunabhängige Schrödingergleichung +\end{block}} +\uncover<6->{% +\begin{block}{Zeitabhängigkeit = Schrödingergleichung} +\[ +-\frac{\hbar}{i} +\frac{\partial}{\partial t} +\psi(x,t) += +-\frac{\hbar^2}{2m}\Delta\psi(x,t) + V(x)\psi(x,t) +\] +\uncover<7->{Eigenwertgleichung durch Separation von $t$} +\end{block}} +\end{column} +\end{columns} +\end{frame} +\egroup |