diff --git a/src/presentation/main.md b/src/presentation/main.md index 3e01254..f207914 100644 --- a/src/presentation/main.md +++ b/src/presentation/main.md @@ -94,3 +94,94 @@ $$ k = \frac{2*\pi*p}{h}, \omega = \frac{2 * \pi * v * p}{h} $$ ;$$ \Psi = A*\circlearrowleft(\frac{2 * \pi * p}{h}*x - \frac{2 * \pi * v * p}{h} * t) $$ ;$$ \Psi = A*\circlearrowleft(\frac{2*\pi*p}{h}*(x - v*t)) \textcolor{red}{= A*e^{\frac{i*p}{\hbar}*(x-v*t)}} $$ + +---- + +### Energieerhaltungssatz + +$$ \Psi = A*\circlearrowleft(\frac{2*\pi*p}{h}*(x - v*t)) \textcolor{red}{= A*e^{\frac{i*p}{\hbar}*(x-v*t)}} $$ +;$$ E_{ges} = E_{kin} + E_{pot} = \frac{p^2}{2*m} + V $$ +;$$ E_{ges} *\Psi = \frac{p^2}{2*m} * \Psi + V * \Psi $$ + +--- + +### Energieerhaltungssatz + +$$ \Psi = A*\circlearrowleft(\frac{2*\pi*p}{h}*(x - v*t)) \textcolor{red}{= A*e^{\frac{i*p}{\hbar}*(x-v*t)}} $$ + +$$ E_{ges} *\Psi = \frac{p^2}{2*m} * \Psi + V * \Psi $$ +;$$ \frac{\partial \Psi}{\partial x} = \circlearrowleft(90\degree) * \frac{2*\pi*p}{h} * \Psi \textcolor{red}{= +\frac{i*p}{\hbar} * \Psi} $$ +;$$ p = \circlearrowleft(-90\degree) * \frac{h}{2*\pi} * \frac{\partial \Psi}{\partial x} \textcolor{red}{= +-i * \hbar * \frac{\partial \Psi}{\partial x}} $$ + +--- + +### Energieerhaltungssatz + +$$ \Psi = A*\circlearrowleft(\frac{2*\pi*p}{h}*(x - v*t)) \textcolor{red}{= A*e^{\frac{i*p}{\hbar}*(x-v*t)}} $$ + +$$ E_{ges} *\Psi = \circlearrowleft(180\degree) * \frac{h^2}{8*m*\pi^2} * \frac{\partial^2 \Psi}{\partial^2 x} + V * +\Psi $$ +; +
+ $$ E_{ges} *\Psi =- \frac{h^2}{8*m*\pi^2} * \frac{\partial^2 \Psi}{\partial^2 x} + V *\Psi + \textcolor{red}{=-\frac{\hbar^2}{2*m} * \frac{\partial^2 \Psi}{\partial^2 x} + V * \Psi } $$ +
+ +--- + +### Energieerhaltungssatz + +
+ $$ E_{ges} *\Psi =- \frac{h^2}{8*m*\pi^2} * \frac{\partial^2 \Psi}{\partial^2 x} + V *\Psi + \textcolor{red}{=-\frac{\hbar^2}{2*m} * \frac{\partial^2 \Psi}{\partial^2 x} + V * \Psi } $$ +
+ +$$ \Psi = A*\circlearrowleft(\frac{2*\pi*p}{h}*(x - v*t)) \textcolor{red}{= A*e^{\frac{i*p}{\hbar}*(x-v*t)}} $$ + +;$$ E_{ph} = h*f = \frac{h*v}{\lambda} = \frac{h*v*p}{h} = v*p $$ +;$$ \frac{\partial \Psi}{\partial t} = -\circlearrowleft(90\degree) * \frac{2*\pi*p * v}{h} * \Psi$$ + +--- + +### Energieerhaltungssatz + +
+ $$ E_{ges} *\Psi =- \frac{h^2}{8*m*\pi^2} * \frac{\partial^2 \Psi}{\partial^2 x} + V *\Psi + \textcolor{red}{=-\frac{\hbar^2}{2*m} * \frac{\partial^2 \Psi}{\partial^2 x} + V * \Psi } $$ +
+ +$$ \Psi = A*\circlearrowleft(\frac{2*\pi*p}{h}*(x - v*t)) \textcolor{red}{= A*e^{\frac{i*p}{\hbar}*(x-v*t)}} $$ + +$$ \frac{\partial \Psi}{\partial t} = -\circlearrowleft(90\degree) * \frac{2*\pi*p * v}{h} * \Psi$$ + +;$$ p*v*\Psi = -\frac{\partial \Psi}{\partial t} * \frac{h}{2*\pi*\circlearrowleft(90\degree)}$$ + +--- + +### Energieerhaltungssatz + +
+ $$ E_{ges} *\Psi =- \frac{h^2}{8*m*\pi^2} * \frac{\partial^2 \Psi}{\partial^2 x} + V *\Psi + \textcolor{red}{=-\frac{\hbar^2}{2*m} * \frac{\partial^2 \Psi}{\partial^2 x} + V * \Psi } $$ +
+ +$$ \Psi = A*\circlearrowleft(\frac{2*\pi*p}{h}*(x - v*t)) \textcolor{red}{= A*e^{\frac{i*p}{\hbar}*(x-v*t)}} $$ + +$$ p*v*\Psi = -\frac{\partial \Psi}{\partial t} * \frac{h}{2*\pi*\circlearrowleft(90\degree)}$$ +;$$ E_{ges} *\Psi = \circlearrowleft(90\degree)* \frac{h}{2*\pi} * \frac{\partial \Psi}{\partial t} \textcolor{red}{ = +i*\hbar*\frac{\partial \Psi}{\partial t}}$$ + +--- + +### Die Schr"odinger Gleichung + +
+ $$ \circlearrowleft(90\degree)* \frac{h}{2*\pi} * \frac{\partial \Psi}{\partial t} =- \frac{h^2}{8*m*\pi^2} * + \frac{\partial^2 \Psi}{\partial^2 x} + V *\Psi $$ +
+
+ $$\textcolor{red}{i*\hbar*\frac{\partial \Psi}{\partial t}=-\frac{\hbar^2}{2*m} * \frac{\partial^2 \Psi}{\partial^2 + x} + V * \Psi } $$ +
diff --git a/src/presentation/main.md b/src/presentation/main.md index 3e01254..f207914 100644 --- a/src/presentation/main.md +++ b/src/presentation/main.md @@ -94,3 +94,94 @@ $$ k = \frac{2*\pi*p}{h}, \omega = \frac{2 * \pi * v * p}{h} $$ ;$$ \Psi = A*\circlearrowleft(\frac{2 * \pi * p}{h}*x - \frac{2 * \pi * v * p}{h} * t) $$ ;$$ \Psi = A*\circlearrowleft(\frac{2*\pi*p}{h}*(x - v*t)) \textcolor{red}{= A*e^{\frac{i*p}{\hbar}*(x-v*t)}} $$ + +---- + +### Energieerhaltungssatz + +$$ \Psi = A*\circlearrowleft(\frac{2*\pi*p}{h}*(x - v*t)) \textcolor{red}{= A*e^{\frac{i*p}{\hbar}*(x-v*t)}} $$ +;$$ E_{ges} = E_{kin} + E_{pot} = \frac{p^2}{2*m} + V $$ +;$$ E_{ges} *\Psi = \frac{p^2}{2*m} * \Psi + V * \Psi $$ + +--- + +### Energieerhaltungssatz + +$$ \Psi = A*\circlearrowleft(\frac{2*\pi*p}{h}*(x - v*t)) \textcolor{red}{= A*e^{\frac{i*p}{\hbar}*(x-v*t)}} $$ + +$$ E_{ges} *\Psi = \frac{p^2}{2*m} * \Psi + V * \Psi $$ +;$$ \frac{\partial \Psi}{\partial x} = \circlearrowleft(90\degree) * \frac{2*\pi*p}{h} * \Psi \textcolor{red}{= +\frac{i*p}{\hbar} * \Psi} $$ +;$$ p = \circlearrowleft(-90\degree) * \frac{h}{2*\pi} * \frac{\partial \Psi}{\partial x} \textcolor{red}{= +-i * \hbar * \frac{\partial \Psi}{\partial x}} $$ + +--- + +### Energieerhaltungssatz + +$$ \Psi = A*\circlearrowleft(\frac{2*\pi*p}{h}*(x - v*t)) \textcolor{red}{= A*e^{\frac{i*p}{\hbar}*(x-v*t)}} $$ + +$$ E_{ges} *\Psi = \circlearrowleft(180\degree) * \frac{h^2}{8*m*\pi^2} * \frac{\partial^2 \Psi}{\partial^2 x} + V * +\Psi $$ +; +
+ $$ E_{ges} *\Psi =- \frac{h^2}{8*m*\pi^2} * \frac{\partial^2 \Psi}{\partial^2 x} + V *\Psi + \textcolor{red}{=-\frac{\hbar^2}{2*m} * \frac{\partial^2 \Psi}{\partial^2 x} + V * \Psi } $$ +
+ +--- + +### Energieerhaltungssatz + +
+ $$ E_{ges} *\Psi =- \frac{h^2}{8*m*\pi^2} * \frac{\partial^2 \Psi}{\partial^2 x} + V *\Psi + \textcolor{red}{=-\frac{\hbar^2}{2*m} * \frac{\partial^2 \Psi}{\partial^2 x} + V * \Psi } $$ +
+ +$$ \Psi = A*\circlearrowleft(\frac{2*\pi*p}{h}*(x - v*t)) \textcolor{red}{= A*e^{\frac{i*p}{\hbar}*(x-v*t)}} $$ + +;$$ E_{ph} = h*f = \frac{h*v}{\lambda} = \frac{h*v*p}{h} = v*p $$ +;$$ \frac{\partial \Psi}{\partial t} = -\circlearrowleft(90\degree) * \frac{2*\pi*p * v}{h} * \Psi$$ + +--- + +### Energieerhaltungssatz + +
+ $$ E_{ges} *\Psi =- \frac{h^2}{8*m*\pi^2} * \frac{\partial^2 \Psi}{\partial^2 x} + V *\Psi + \textcolor{red}{=-\frac{\hbar^2}{2*m} * \frac{\partial^2 \Psi}{\partial^2 x} + V * \Psi } $$ +
+ +$$ \Psi = A*\circlearrowleft(\frac{2*\pi*p}{h}*(x - v*t)) \textcolor{red}{= A*e^{\frac{i*p}{\hbar}*(x-v*t)}} $$ + +$$ \frac{\partial \Psi}{\partial t} = -\circlearrowleft(90\degree) * \frac{2*\pi*p * v}{h} * \Psi$$ + +;$$ p*v*\Psi = -\frac{\partial \Psi}{\partial t} * \frac{h}{2*\pi*\circlearrowleft(90\degree)}$$ + +--- + +### Energieerhaltungssatz + +
+ $$ E_{ges} *\Psi =- \frac{h^2}{8*m*\pi^2} * \frac{\partial^2 \Psi}{\partial^2 x} + V *\Psi + \textcolor{red}{=-\frac{\hbar^2}{2*m} * \frac{\partial^2 \Psi}{\partial^2 x} + V * \Psi } $$ +
+ +$$ \Psi = A*\circlearrowleft(\frac{2*\pi*p}{h}*(x - v*t)) \textcolor{red}{= A*e^{\frac{i*p}{\hbar}*(x-v*t)}} $$ + +$$ p*v*\Psi = -\frac{\partial \Psi}{\partial t} * \frac{h}{2*\pi*\circlearrowleft(90\degree)}$$ +;$$ E_{ges} *\Psi = \circlearrowleft(90\degree)* \frac{h}{2*\pi} * \frac{\partial \Psi}{\partial t} \textcolor{red}{ = +i*\hbar*\frac{\partial \Psi}{\partial t}}$$ + +--- + +### Die Schr"odinger Gleichung + +
+ $$ \circlearrowleft(90\degree)* \frac{h}{2*\pi} * \frac{\partial \Psi}{\partial t} =- \frac{h^2}{8*m*\pi^2} * + \frac{\partial^2 \Psi}{\partial^2 x} + V *\Psi $$ +
+
+ $$\textcolor{red}{i*\hbar*\frac{\partial \Psi}{\partial t}=-\frac{\hbar^2}{2*m} * \frac{\partial^2 \Psi}{\partial^2 + x} + V * \Psi } $$ +
diff --git a/src/template_presentation.html b/src/template_presentation.html index 3df0e52..f0a34c0 100644 --- a/src/template_presentation.html +++ b/src/template_presentation.html @@ -22,6 +22,10 @@ .katex-display { scale: 80%; } + + .small { + scale: 80%; + }