diff --git a/src/build.js b/src/build.js index 0361a7d..01ddd65 100644 --- a/src/build.js +++ b/src/build.js @@ -6,9 +6,11 @@ "../../node_modules/reveal.js/dist/reveal.css": "build/css/", "../../node_modules/reveal.js/dist/theme/moon.css": "build/css/", "../../node_modules/reveal.js/dist/reveal.js": "build/js/", + "../../node_modules/reveal.js/plugin/math/math.js": "build/js/", "../../src/static/css/style.css": "build/css/", "../../src/static/video/oscillator.mp4": "build/video", "../../src/static/video/travelling.mp4": "build/video", + "../../src/static/video/photon.mp4": "build/video", } const buildFolder = "build" diff --git a/src/build.js b/src/build.js index 0361a7d..01ddd65 100644 --- a/src/build.js +++ b/src/build.js @@ -6,9 +6,11 @@ "../../node_modules/reveal.js/dist/reveal.css": "build/css/", "../../node_modules/reveal.js/dist/theme/moon.css": "build/css/", "../../node_modules/reveal.js/dist/reveal.js": "build/js/", + "../../node_modules/reveal.js/plugin/math/math.js": "build/js/", "../../src/static/css/style.css": "build/css/", "../../src/static/video/oscillator.mp4": "build/video", "../../src/static/video/travelling.mp4": "build/video", + "../../src/static/video/photon.mp4": "build/video", } const buildFolder = "build" diff --git a/src/presentation/main.md b/src/presentation/main.md deleted file mode 100644 index f207914..0000000 --- a/src/presentation/main.md +++ /dev/null @@ -1,187 +0,0 @@ -%English -## The Schrodinger Equation -%German -## Die Schr"odinger Gleichung - ----- - -### Die harmonische Schwingung - -$$ a = \frac{d v}{dt} = \frac{F}{m} = -\frac{D*x}{m} = \frac{d^2 x}{d^2 t}$$ -;$$ x = A*\cos(\omega * t) \Leftrightarrow \frac{d^2 x}{d^2 t} = -\frac{D*x}{m} = -\omega^2 * x $$ -;$$\omega = \sqrt{\frac{D}{m}}$$ - ---- - -### Die harmonische Schwingung - -$$ x = A*\cos(\sqrt{\frac{D}{m}} * t) $$ -;$$ v = \frac{d x}{d t} = \omega * A * \sin(\sqrt{\frac{D}{m}} * t)$$ -;$$ E_{kin} = \frac{1}{2} * m * v^2 = \frac{1}{2} * D * A^2 * \sin^2(\omega * t)$$ -;$$ E_{Feder} = \frac{1}{2} * D * x^2 = \frac{1}{2} * D * A^2 * \cos^2(\omega * t)$$ - ---- - -### Die harmonische Schwingung - -$$ E_{kin} = \frac{1}{2} * m * v^2 = \frac{1}{2} * D * A^2 * \sin^2(\omega * t)$$ - -$$ E_{Feder} = \frac{1}{2} * D * x^2 = \frac{1}{2} * D * A^2 * \cos^2(\omega * t)$$ - -;$$ E_{ges} = E_{kin} + E_{Feder} = \frac{1}{2} * D * A^2 * $$ -$$(\sin^2(\omega * t) + \cos^2(\omega * t)) = \frac{1}{2} * D * A^2 $$ - ---- - -### Die harmonische Schwingung - -$$ E_{ges} = \frac{1}{2} * D * A^2 $$ - -;$$ \Psi = \sqrt{\frac{D}{2}}*\begin{pmatrix} x \\ \frac{v}{\omega} \end{pmatrix} = \sqrt{\frac{D}{2}}*\begin{pmatrix} -A*\cos(\omega * t) \\ \frac{\omega * A * \sin(\omega * t)}{\omega}\end{pmatrix}$$ -;$$ \Psi = \sqrt{\frac{D}{2}}*\begin{pmatrix} A \\ A \end{pmatrix} \odot \circlearrowleft(\omega * t) -= \sqrt{\frac{D}{2}}*A *\circlearrowleft(\omega * t) $$ - ---- - -### Die harmonische Schwingung - -$$ \Psi = \sqrt{\frac{D}{2}}*\begin{pmatrix} A \\ A \end{pmatrix} \odot \circlearrowleft(\omega * t) -= \sqrt{\frac{D}{2}}*A *\circlearrowleft(\omega * t) $$ -$$ \textcolor{red}{\Psi=\sqrt{\frac{D}{2}} * A * e^{i*\omega*t}}$$ -;$$|\Psi|^2 = E_{ges} = \frac{D*A^2}2 $$ - ---- - -### Die harmonische Schwingung - - ----- - -### Wanderwelle - - - ---- - -### Wanderwelle - - - -$$ \Psi = A*\circlearrowleft(k*x - \omega * t) \textcolor{red}{= A*e^{i(k*x-\omega*t)}}$$ - ---- - -### Wanderwelle - -$$ \Psi = A*\circlearrowleft(k*x - \omega * t) \textcolor{red}{= A*e^{i(k*x-\omega*t)}}$$ -;$$ k = \frac{2*\pi}{\lambda}, \omega = 2*\pi*f $$ -;$$ \lambda = \frac{h}{p} \Rightarrow k = \frac{2*\pi*p}{h} $$ -;$$ \omega = 2 * \pi * \frac{v}{\lambda} = \frac{2 * \pi * v * p}{h} $$ - ---- - -### Wanderwelle - -$$ \Psi = A*\circlearrowleft(k*x - \omega * t) \textcolor{red}{= A*e^{i(k*x-\omega*t)}}$$ - -$$ k = \frac{2*\pi*p}{h}, \omega = \frac{2 * \pi * v * p}{h} $$ -;$$ \Psi = A*\circlearrowleft(\frac{2 * \pi * p}{h}*x - \frac{2 * \pi * v * p}{h} * t) $$ -;$$ \Psi = A*\circlearrowleft(\frac{2*\pi*p}{h}*(x - v*t)) \textcolor{red}{= A*e^{\frac{i*p}{\hbar}*(x-v*t)}} $$ - ----- - -### 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/build.js b/src/build.js index 0361a7d..01ddd65 100644 --- a/src/build.js +++ b/src/build.js @@ -6,9 +6,11 @@ "../../node_modules/reveal.js/dist/reveal.css": "build/css/", "../../node_modules/reveal.js/dist/theme/moon.css": "build/css/", "../../node_modules/reveal.js/dist/reveal.js": "build/js/", + "../../node_modules/reveal.js/plugin/math/math.js": "build/js/", "../../src/static/css/style.css": "build/css/", "../../src/static/video/oscillator.mp4": "build/video", "../../src/static/video/travelling.mp4": "build/video", + "../../src/static/video/photon.mp4": "build/video", } const buildFolder = "build" diff --git a/src/presentation/main.md b/src/presentation/main.md deleted file mode 100644 index f207914..0000000 --- a/src/presentation/main.md +++ /dev/null @@ -1,187 +0,0 @@ -%English -## The Schrodinger Equation -%German -## Die Schr"odinger Gleichung - ----- - -### Die harmonische Schwingung - -$$ a = \frac{d v}{dt} = \frac{F}{m} = -\frac{D*x}{m} = \frac{d^2 x}{d^2 t}$$ -;$$ x = A*\cos(\omega * t) \Leftrightarrow \frac{d^2 x}{d^2 t} = -\frac{D*x}{m} = -\omega^2 * x $$ -;$$\omega = \sqrt{\frac{D}{m}}$$ - ---- - -### Die harmonische Schwingung - -$$ x = A*\cos(\sqrt{\frac{D}{m}} * t) $$ -;$$ v = \frac{d x}{d t} = \omega * A * \sin(\sqrt{\frac{D}{m}} * t)$$ -;$$ E_{kin} = \frac{1}{2} * m * v^2 = \frac{1}{2} * D * A^2 * \sin^2(\omega * t)$$ -;$$ E_{Feder} = \frac{1}{2} * D * x^2 = \frac{1}{2} * D * A^2 * \cos^2(\omega * t)$$ - ---- - -### Die harmonische Schwingung - -$$ E_{kin} = \frac{1}{2} * m * v^2 = \frac{1}{2} * D * A^2 * \sin^2(\omega * t)$$ - -$$ E_{Feder} = \frac{1}{2} * D * x^2 = \frac{1}{2} * D * A^2 * \cos^2(\omega * t)$$ - -;$$ E_{ges} = E_{kin} + E_{Feder} = \frac{1}{2} * D * A^2 * $$ -$$(\sin^2(\omega * t) + \cos^2(\omega * t)) = \frac{1}{2} * D * A^2 $$ - ---- - -### Die harmonische Schwingung - -$$ E_{ges} = \frac{1}{2} * D * A^2 $$ - -;$$ \Psi = \sqrt{\frac{D}{2}}*\begin{pmatrix} x \\ \frac{v}{\omega} \end{pmatrix} = \sqrt{\frac{D}{2}}*\begin{pmatrix} -A*\cos(\omega * t) \\ \frac{\omega * A * \sin(\omega * t)}{\omega}\end{pmatrix}$$ -;$$ \Psi = \sqrt{\frac{D}{2}}*\begin{pmatrix} A \\ A \end{pmatrix} \odot \circlearrowleft(\omega * t) -= \sqrt{\frac{D}{2}}*A *\circlearrowleft(\omega * t) $$ - ---- - -### Die harmonische Schwingung - -$$ \Psi = \sqrt{\frac{D}{2}}*\begin{pmatrix} A \\ A \end{pmatrix} \odot \circlearrowleft(\omega * t) -= \sqrt{\frac{D}{2}}*A *\circlearrowleft(\omega * t) $$ -$$ \textcolor{red}{\Psi=\sqrt{\frac{D}{2}} * A * e^{i*\omega*t}}$$ -;$$|\Psi|^2 = E_{ges} = \frac{D*A^2}2 $$ - ---- - -### Die harmonische Schwingung - - ----- - -### Wanderwelle - - - ---- - -### Wanderwelle - - - -$$ \Psi = A*\circlearrowleft(k*x - \omega * t) \textcolor{red}{= A*e^{i(k*x-\omega*t)}}$$ - ---- - -### Wanderwelle - -$$ \Psi = A*\circlearrowleft(k*x - \omega * t) \textcolor{red}{= A*e^{i(k*x-\omega*t)}}$$ -;$$ k = \frac{2*\pi}{\lambda}, \omega = 2*\pi*f $$ -;$$ \lambda = \frac{h}{p} \Rightarrow k = \frac{2*\pi*p}{h} $$ -;$$ \omega = 2 * \pi * \frac{v}{\lambda} = \frac{2 * \pi * v * p}{h} $$ - ---- - -### Wanderwelle - -$$ \Psi = A*\circlearrowleft(k*x - \omega * t) \textcolor{red}{= A*e^{i(k*x-\omega*t)}}$$ - -$$ k = \frac{2*\pi*p}{h}, \omega = \frac{2 * \pi * v * p}{h} $$ -;$$ \Psi = A*\circlearrowleft(\frac{2 * \pi * p}{h}*x - \frac{2 * \pi * v * p}{h} * t) $$ -;$$ \Psi = A*\circlearrowleft(\frac{2*\pi*p}{h}*(x - v*t)) \textcolor{red}{= A*e^{\frac{i*p}{\hbar}*(x-v*t)}} $$ - ----- - -### 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/python/photon.py b/src/python/photon.py new file mode 100644 index 0000000..eb6a715 --- /dev/null +++ b/src/python/photon.py @@ -0,0 +1,28 @@ +import numpy as np +import matplotlib.pyplot as plt +import matplotlib.animation as animation + +outputFolder = "src/static/video/" + +totalTime = 12 +framerate = 20 + +psi = lambda x,t,n: np.sin(n*np.pi*x) * np.exp(-0.25j*n**2*np.pi*t) + +wave = lambda x, t: np.abs(psi(x, t, 1) + psi(x, t, 2))**2 + +fig, ax = plt.subplots() + +x = np.linspace(0, 1, 100) +line, = ax.plot(x, wave(x, 0)) + +def animate(i): + t = i/framerate + line.set_ydata(wave(x, t)) + return line, + + +ani = animation.FuncAnimation( + fig, animate, interval=1000/framerate, blit=True, save_count = framerate * totalTime) +ani.save(f"{outputFolder}photon.mp4") +plt.show() diff --git a/src/build.js b/src/build.js index 0361a7d..01ddd65 100644 --- a/src/build.js +++ b/src/build.js @@ -6,9 +6,11 @@ "../../node_modules/reveal.js/dist/reveal.css": "build/css/", "../../node_modules/reveal.js/dist/theme/moon.css": "build/css/", "../../node_modules/reveal.js/dist/reveal.js": "build/js/", + "../../node_modules/reveal.js/plugin/math/math.js": "build/js/", "../../src/static/css/style.css": "build/css/", "../../src/static/video/oscillator.mp4": "build/video", "../../src/static/video/travelling.mp4": "build/video", + "../../src/static/video/photon.mp4": "build/video", } const buildFolder = "build" diff --git a/src/presentation/main.md b/src/presentation/main.md deleted file mode 100644 index f207914..0000000 --- a/src/presentation/main.md +++ /dev/null @@ -1,187 +0,0 @@ -%English -## The Schrodinger Equation -%German -## Die Schr"odinger Gleichung - ----- - -### Die harmonische Schwingung - -$$ a = \frac{d v}{dt} = \frac{F}{m} = -\frac{D*x}{m} = \frac{d^2 x}{d^2 t}$$ -;$$ x = A*\cos(\omega * t) \Leftrightarrow \frac{d^2 x}{d^2 t} = -\frac{D*x}{m} = -\omega^2 * x $$ -;$$\omega = \sqrt{\frac{D}{m}}$$ - ---- - -### Die harmonische Schwingung - -$$ x = A*\cos(\sqrt{\frac{D}{m}} * t) $$ -;$$ v = \frac{d x}{d t} = \omega * A * \sin(\sqrt{\frac{D}{m}} * t)$$ -;$$ E_{kin} = \frac{1}{2} * m * v^2 = \frac{1}{2} * D * A^2 * \sin^2(\omega * t)$$ -;$$ E_{Feder} = \frac{1}{2} * D * x^2 = \frac{1}{2} * D * A^2 * \cos^2(\omega * t)$$ - ---- - -### Die harmonische Schwingung - -$$ E_{kin} = \frac{1}{2} * m * v^2 = \frac{1}{2} * D * A^2 * \sin^2(\omega * t)$$ - -$$ E_{Feder} = \frac{1}{2} * D * x^2 = \frac{1}{2} * D * A^2 * \cos^2(\omega * t)$$ - -;$$ E_{ges} = E_{kin} + E_{Feder} = \frac{1}{2} * D * A^2 * $$ -$$(\sin^2(\omega * t) + \cos^2(\omega * t)) = \frac{1}{2} * D * A^2 $$ - ---- - -### Die harmonische Schwingung - -$$ E_{ges} = \frac{1}{2} * D * A^2 $$ - -;$$ \Psi = \sqrt{\frac{D}{2}}*\begin{pmatrix} x \\ \frac{v}{\omega} \end{pmatrix} = \sqrt{\frac{D}{2}}*\begin{pmatrix} -A*\cos(\omega * t) \\ \frac{\omega * A * \sin(\omega * t)}{\omega}\end{pmatrix}$$ -;$$ \Psi = \sqrt{\frac{D}{2}}*\begin{pmatrix} A \\ A \end{pmatrix} \odot \circlearrowleft(\omega * t) -= \sqrt{\frac{D}{2}}*A *\circlearrowleft(\omega * t) $$ - ---- - -### Die harmonische Schwingung - -$$ \Psi = \sqrt{\frac{D}{2}}*\begin{pmatrix} A \\ A \end{pmatrix} \odot \circlearrowleft(\omega * t) -= \sqrt{\frac{D}{2}}*A *\circlearrowleft(\omega * t) $$ -$$ \textcolor{red}{\Psi=\sqrt{\frac{D}{2}} * A * e^{i*\omega*t}}$$ -;$$|\Psi|^2 = E_{ges} = \frac{D*A^2}2 $$ - ---- - -### Die harmonische Schwingung - - ----- - -### Wanderwelle - - - ---- - -### Wanderwelle - - - -$$ \Psi = A*\circlearrowleft(k*x - \omega * t) \textcolor{red}{= A*e^{i(k*x-\omega*t)}}$$ - ---- - -### Wanderwelle - -$$ \Psi = A*\circlearrowleft(k*x - \omega * t) \textcolor{red}{= A*e^{i(k*x-\omega*t)}}$$ -;$$ k = \frac{2*\pi}{\lambda}, \omega = 2*\pi*f $$ -;$$ \lambda = \frac{h}{p} \Rightarrow k = \frac{2*\pi*p}{h} $$ -;$$ \omega = 2 * \pi * \frac{v}{\lambda} = \frac{2 * \pi * v * p}{h} $$ - ---- - -### Wanderwelle - -$$ \Psi = A*\circlearrowleft(k*x - \omega * t) \textcolor{red}{= A*e^{i(k*x-\omega*t)}}$$ - -$$ k = \frac{2*\pi*p}{h}, \omega = \frac{2 * \pi * v * p}{h} $$ -;$$ \Psi = A*\circlearrowleft(\frac{2 * \pi * p}{h}*x - \frac{2 * \pi * v * p}{h} * t) $$ -;$$ \Psi = A*\circlearrowleft(\frac{2*\pi*p}{h}*(x - v*t)) \textcolor{red}{= A*e^{\frac{i*p}{\hbar}*(x-v*t)}} $$ - ----- - -### 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/python/photon.py b/src/python/photon.py new file mode 100644 index 0000000..eb6a715 --- /dev/null +++ b/src/python/photon.py @@ -0,0 +1,28 @@ +import numpy as np +import matplotlib.pyplot as plt +import matplotlib.animation as animation + +outputFolder = "src/static/video/" + +totalTime = 12 +framerate = 20 + +psi = lambda x,t,n: np.sin(n*np.pi*x) * np.exp(-0.25j*n**2*np.pi*t) + +wave = lambda x, t: np.abs(psi(x, t, 1) + psi(x, t, 2))**2 + +fig, ax = plt.subplots() + +x = np.linspace(0, 1, 100) +line, = ax.plot(x, wave(x, 0)) + +def animate(i): + t = i/framerate + line.set_ydata(wave(x, t)) + return line, + + +ani = animation.FuncAnimation( + fig, animate, interval=1000/framerate, blit=True, save_count = framerate * totalTime) +ani.save(f"{outputFolder}photon.mp4") +plt.show() diff --git a/src/template_presentation.html b/src/template_presentation.html index f0a34c0..76d0c21 100644 --- a/src/template_presentation.html +++ b/src/template_presentation.html @@ -10,17 +10,12 @@ - - - +