diff --git a/src/build.js b/src/build.js
index f1b84fa..ef07030 100644
--- a/src/build.js
+++ b/src/build.js
@@ -9,6 +9,7 @@
"../../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/oscillator_simple.mp4": "build/video",
"../../src/static/video/travelling.mp4": "build/video",
"../../src/static/video/photon.mp4": "build/video",
"../../src/static/video/doubleSlit.mp4": "build/video",
diff --git a/src/build.js b/src/build.js
index f1b84fa..ef07030 100644
--- a/src/build.js
+++ b/src/build.js
@@ -9,6 +9,7 @@
"../../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/oscillator_simple.mp4": "build/video",
"../../src/static/video/travelling.mp4": "build/video",
"../../src/static/video/photon.mp4": "build/video",
"../../src/static/video/doubleSlit.mp4": "build/video",
diff --git a/src/presentation/main.md b/src/presentation/main.md
index fc09d86..d7d71e2 100644
--- a/src/presentation/main.md
+++ b/src/presentation/main.md
@@ -7,6 +7,15 @@
### Die harmonische Schwingung
+
+
+
+---
+
+### Die harmonische Schwingung
+
$$ a = \frac{d v}{dt} = \frac{F}{m} = -\frac{D*x}{m} = \frac{d^2 x}{d^2 t}$$
;$$ x = A*\cos(\omega * t) \Leftrightarrow \frac{d^2 x}{d^2 t} = -\frac{D*x}{m} = -\omega^2 * x $$
;$$\omega = \sqrt{\frac{D}{m}}$$
@@ -193,7 +202,7 @@
$$ V = 0 \forall x \in [0; l], V = \infty \forall x \notin [0; l] $$
-;$$ \Psi = 0 \forall x \notin [0, l], \Psi \in \mathbb{C} \forall x \in [0, l] $$
+;$$ \Psi \in \mathbb{C} \forall x \in [0, l], \Psi = 0 \forall x \notin [0, l] $$
;$$ \Psi = \Psi_x * \Psi_t $$
---
@@ -283,45 +292,14 @@
;$$ \Psi = \int_{-\infty}^{\infty} \psi* \circlearrowleft(k*x)* dk \textcolor{red}{=\int_{-\infty}^{\infty} \psi*
e^{i*k*x}*dk}$$
-;$$ \Psi = \int \int \circlearrowleft(-k*x)*dx * \circlearrowleft(k*x)*dk * \Psi$$
-;$$ \psi = \int \circlearrowleft(-k*x)*\Psi*dx \textcolor{red}{=\int_{-\infty}^{\infty} \Psi*
+;$$ \Psi = \int_{-\infty}^{\infty} \circlearrowleft(k*x)*dk * \int_{-\infty}^{\infty} \circlearrowleft(-k*x)*\Psi*dx $$
+;$$ \psi = \int_{-\infty}^{\infty} \circlearrowleft(-k*x)*\Psi*dx \textcolor{red}{=\int_{-\infty}^{\infty} \Psi*
e^{-i*k*x}*dk}$$
---
### Impulsraum
-$$ \Psi = \int_{-\infty}^{\infty} \psi* \circlearrowleft(k*x)* dk \textcolor{red}{=\int_{-\infty}^{\infty} \psi*
-e^{i*k*x}*dk}$$
-
-;$$ \frac{\partial \Psi}{\partial k} = \psi* \circlearrowleft(k*x) \textcolor{red}{= \psi* e^{i*k*x}}$$
-;$$ \psi = \frac{\partial}{\partial k}* \circlearrowleft(-k*x)* \Psi \textcolor{red}{= \frac{\partial
-}{\partial k}* e^{-i*k*x} * \Psi}$$
-;$$ \psi = \circlearrowleft(-90\degree) * \circlearrowleft(-k*x)* \Psi \textcolor{red}{= -i*x* e^{-i*k*x} * \Psi}$$
-;$$ \int \psi *dx = \int \circlearrowleft(-90\degree) * \circlearrowleft(-k*x)* \Psi * dx \textcolor{red}{= \int -i*x*
-e^{-i*k*x} * \Psi *dx}$$
-;$$ F(x*\Psi) = \circlearrowleft(90\degree) * F(\Psi)\textcolor{red}{= i*F(\Psi)} $$
-
----
-
-### Impulsraum
-
-$$ \Psi = \int_{-\infty}^{\infty} \psi* \circlearrowleft(k*x)* dk \textcolor{red}{=\int_{-\infty}^{\infty} \psi*
-e^{i*k*x}*dk}$$
-
-$$ \psi = F(\Psi) = \int_{-\infty}^{\infty} \circlearrowleft(-k*x)*\Psi*dx \textcolor{red}{=\int_{-\infty}^{\infty}
-\Psi*e^{-i*k*x}*dk}$$
-
-$$ \frac{\partial \psi}{\partial k} = \int \frac{\partial}{\partial k}\circlearrowleft(-k*x)*\Psi*dx
-\textcolor{red}{=\int_{-\infty}^{\infty} \Psi*\frac{\partial}{\partial k}e^{-i*k*x}*dk} $$
-;$$ \frac{\partial \psi}{\partial k} = \int x*\circlearrowleft(-90\degree) * \circlearrowleft(-k*x)*\Psi*dx
-\textcolor{red}{=\int_{-\infty}^{\infty} -i*x*\Psi*e^{-i*k*x}*dk} $$
-;$$ \frac{\partial \psi}{\partial k} = \circlearrowleft(-90\degree)*F^{-1}(\Psi*k)\textcolor{red}{=-i*F^{-1}(\Psi*k)} $$
-
----
-
-### Impulsraum
-
$$ \psi = F(\Psi) = \int_{-\infty}^{\infty} \circlearrowleft(-k*x)*\Psi*dx \textcolor{red}{=\int_{-\infty}^{\infty}
\Psi*e^{-i*k*x}*dk}$$
diff --git a/src/build.js b/src/build.js
index f1b84fa..ef07030 100644
--- a/src/build.js
+++ b/src/build.js
@@ -9,6 +9,7 @@
"../../node_modules/reveal.js/plugin/math/math.js": "build/js/",
"../../src/static/css/style.css": "build/css/",
"../../src/static/video/oscillator.mp4": "build/video",
+ "../../src/static/video/oscillator_simple.mp4": "build/video",
"../../src/static/video/travelling.mp4": "build/video",
"../../src/static/video/photon.mp4": "build/video",
"../../src/static/video/doubleSlit.mp4": "build/video",
diff --git a/src/presentation/main.md b/src/presentation/main.md
index fc09d86..d7d71e2 100644
--- a/src/presentation/main.md
+++ b/src/presentation/main.md
@@ -7,6 +7,15 @@
### Die harmonische Schwingung
+
+
+
+---
+
+### Die harmonische Schwingung
+
$$ 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}}$$
@@ -193,7 +202,7 @@
$$ V = 0 \forall x \in [0; l], V = \infty \forall x \notin [0; l] $$
-;$$ \Psi = 0 \forall x \notin [0, l], \Psi \in \mathbb{C} \forall x \in [0, l] $$
+;$$ \Psi \in \mathbb{C} \forall x \in [0, l], \Psi = 0 \forall x \notin [0, l] $$
;$$ \Psi = \Psi_x * \Psi_t $$
---
@@ -283,45 +292,14 @@
;$$ \Psi = \int_{-\infty}^{\infty} \psi* \circlearrowleft(k*x)* dk \textcolor{red}{=\int_{-\infty}^{\infty} \psi*
e^{i*k*x}*dk}$$
-;$$ \Psi = \int \int \circlearrowleft(-k*x)*dx * \circlearrowleft(k*x)*dk * \Psi$$
-;$$ \psi = \int \circlearrowleft(-k*x)*\Psi*dx \textcolor{red}{=\int_{-\infty}^{\infty} \Psi*
+;$$ \Psi = \int_{-\infty}^{\infty} \circlearrowleft(k*x)*dk * \int_{-\infty}^{\infty} \circlearrowleft(-k*x)*\Psi*dx $$
+;$$ \psi = \int_{-\infty}^{\infty} \circlearrowleft(-k*x)*\Psi*dx \textcolor{red}{=\int_{-\infty}^{\infty} \Psi*
e^{-i*k*x}*dk}$$
---
### Impulsraum
-$$ \Psi = \int_{-\infty}^{\infty} \psi* \circlearrowleft(k*x)* dk \textcolor{red}{=\int_{-\infty}^{\infty} \psi*
-e^{i*k*x}*dk}$$
-
-;$$ \frac{\partial \Psi}{\partial k} = \psi* \circlearrowleft(k*x) \textcolor{red}{= \psi* e^{i*k*x}}$$
-;$$ \psi = \frac{\partial}{\partial k}* \circlearrowleft(-k*x)* \Psi \textcolor{red}{= \frac{\partial
-}{\partial k}* e^{-i*k*x} * \Psi}$$
-;$$ \psi = \circlearrowleft(-90\degree) * \circlearrowleft(-k*x)* \Psi \textcolor{red}{= -i*x* e^{-i*k*x} * \Psi}$$
-;$$ \int \psi *dx = \int \circlearrowleft(-90\degree) * \circlearrowleft(-k*x)* \Psi * dx \textcolor{red}{= \int -i*x*
-e^{-i*k*x} * \Psi *dx}$$
-;$$ F(x*\Psi) = \circlearrowleft(90\degree) * F(\Psi)\textcolor{red}{= i*F(\Psi)} $$
-
----
-
-### Impulsraum
-
-$$ \Psi = \int_{-\infty}^{\infty} \psi* \circlearrowleft(k*x)* dk \textcolor{red}{=\int_{-\infty}^{\infty} \psi*
-e^{i*k*x}*dk}$$
-
-$$ \psi = F(\Psi) = \int_{-\infty}^{\infty} \circlearrowleft(-k*x)*\Psi*dx \textcolor{red}{=\int_{-\infty}^{\infty}
-\Psi*e^{-i*k*x}*dk}$$
-
-$$ \frac{\partial \psi}{\partial k} = \int \frac{\partial}{\partial k}\circlearrowleft(-k*x)*\Psi*dx
-\textcolor{red}{=\int_{-\infty}^{\infty} \Psi*\frac{\partial}{\partial k}e^{-i*k*x}*dk} $$
-;$$ \frac{\partial \psi}{\partial k} = \int x*\circlearrowleft(-90\degree) * \circlearrowleft(-k*x)*\Psi*dx
-\textcolor{red}{=\int_{-\infty}^{\infty} -i*x*\Psi*e^{-i*k*x}*dk} $$
-;$$ \frac{\partial \psi}{\partial k} = \circlearrowleft(-90\degree)*F^{-1}(\Psi*k)\textcolor{red}{=-i*F^{-1}(\Psi*k)} $$
-
----
-
-### Impulsraum
-
$$ \psi = F(\Psi) = \int_{-\infty}^{\infty} \circlearrowleft(-k*x)*\Psi*dx \textcolor{red}{=\int_{-\infty}^{\infty}
\Psi*e^{-i*k*x}*dk}$$
diff --git a/src/python/oscillator.py b/src/python/oscillator.py
index c2885de..e99ccfd 100644
--- a/src/python/oscillator.py
+++ b/src/python/oscillator.py
@@ -63,4 +63,20 @@
ani = animation.FuncAnimation(
fig, animate, interval=1000/framerate, blit=True, save_count = framerate * totalTime)
ani.save(f"{outputFolder}oscillator.mp4")
-plt.show()
+
+fig, diagrammAx = plt.subplots()
+
+diagrammAx.axis("equal")
+diagrammAx.set_ylim(-1.5*A, 1.5*A)
+diagrammAx.set_xlim(-1.5*A, 1.5*A)
+diagrammAx.set_xlabel("x")
+diagrammGraph, = diagrammAx.plot([0, 1], [0, 0], "o-")
+
+def animate(i):
+ t = i/framerate
+ x = position(t)
+ diagrammGraph.set_data([0, x], [0, 0])
+ return diagrammGraph,
+ani = animation.FuncAnimation(
+ fig, animate, interval=1000/framerate, blit=True, save_count = framerate * totalTime)
+ani.save(f"{outputFolder}oscillator_simple.mp4")
diff --git a/src/build.js b/src/build.js
index f1b84fa..ef07030 100644
--- a/src/build.js
+++ b/src/build.js
@@ -9,6 +9,7 @@
"../../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/oscillator_simple.mp4": "build/video",
"../../src/static/video/travelling.mp4": "build/video",
"../../src/static/video/photon.mp4": "build/video",
"../../src/static/video/doubleSlit.mp4": "build/video",
diff --git a/src/presentation/main.md b/src/presentation/main.md
index fc09d86..d7d71e2 100644
--- a/src/presentation/main.md
+++ b/src/presentation/main.md
@@ -7,6 +7,15 @@
### Die harmonische Schwingung
+
+
+
+---
+
+### Die harmonische Schwingung
+
$$ a = \frac{d v}{dt} = \frac{F}{m} = -\frac{D*x}{m} = \frac{d^2 x}{d^2 t}$$
;$$ x = A*\cos(\omega * t) \Leftrightarrow \frac{d^2 x}{d^2 t} = -\frac{D*x}{m} = -\omega^2 * x $$
;$$\omega = \sqrt{\frac{D}{m}}$$
@@ -193,7 +202,7 @@
$$ V = 0 \forall x \in [0; l], V = \infty \forall x \notin [0; l] $$
-;$$ \Psi = 0 \forall x \notin [0, l], \Psi \in \mathbb{C} \forall x \in [0, l] $$
+;$$ \Psi \in \mathbb{C} \forall x \in [0, l], \Psi = 0 \forall x \notin [0, l] $$
;$$ \Psi = \Psi_x * \Psi_t $$
---
@@ -283,45 +292,14 @@
;$$ \Psi = \int_{-\infty}^{\infty} \psi* \circlearrowleft(k*x)* dk \textcolor{red}{=\int_{-\infty}^{\infty} \psi*
e^{i*k*x}*dk}$$
-;$$ \Psi = \int \int \circlearrowleft(-k*x)*dx * \circlearrowleft(k*x)*dk * \Psi$$
-;$$ \psi = \int \circlearrowleft(-k*x)*\Psi*dx \textcolor{red}{=\int_{-\infty}^{\infty} \Psi*
+;$$ \Psi = \int_{-\infty}^{\infty} \circlearrowleft(k*x)*dk * \int_{-\infty}^{\infty} \circlearrowleft(-k*x)*\Psi*dx $$
+;$$ \psi = \int_{-\infty}^{\infty} \circlearrowleft(-k*x)*\Psi*dx \textcolor{red}{=\int_{-\infty}^{\infty} \Psi*
e^{-i*k*x}*dk}$$
---
### Impulsraum
-$$ \Psi = \int_{-\infty}^{\infty} \psi* \circlearrowleft(k*x)* dk \textcolor{red}{=\int_{-\infty}^{\infty} \psi*
-e^{i*k*x}*dk}$$
-
-;$$ \frac{\partial \Psi}{\partial k} = \psi* \circlearrowleft(k*x) \textcolor{red}{= \psi* e^{i*k*x}}$$
-;$$ \psi = \frac{\partial}{\partial k}* \circlearrowleft(-k*x)* \Psi \textcolor{red}{= \frac{\partial
-}{\partial k}* e^{-i*k*x} * \Psi}$$
-;$$ \psi = \circlearrowleft(-90\degree) * \circlearrowleft(-k*x)* \Psi \textcolor{red}{= -i*x* e^{-i*k*x} * \Psi}$$
-;$$ \int \psi *dx = \int \circlearrowleft(-90\degree) * \circlearrowleft(-k*x)* \Psi * dx \textcolor{red}{= \int -i*x*
-e^{-i*k*x} * \Psi *dx}$$
-;$$ F(x*\Psi) = \circlearrowleft(90\degree) * F(\Psi)\textcolor{red}{= i*F(\Psi)} $$
-
----
-
-### Impulsraum
-
-$$ \Psi = \int_{-\infty}^{\infty} \psi* \circlearrowleft(k*x)* dk \textcolor{red}{=\int_{-\infty}^{\infty} \psi*
-e^{i*k*x}*dk}$$
-
-$$ \psi = F(\Psi) = \int_{-\infty}^{\infty} \circlearrowleft(-k*x)*\Psi*dx \textcolor{red}{=\int_{-\infty}^{\infty}
-\Psi*e^{-i*k*x}*dk}$$
-
-$$ \frac{\partial \psi}{\partial k} = \int \frac{\partial}{\partial k}\circlearrowleft(-k*x)*\Psi*dx
-\textcolor{red}{=\int_{-\infty}^{\infty} \Psi*\frac{\partial}{\partial k}e^{-i*k*x}*dk} $$
-;$$ \frac{\partial \psi}{\partial k} = \int x*\circlearrowleft(-90\degree) * \circlearrowleft(-k*x)*\Psi*dx
-\textcolor{red}{=\int_{-\infty}^{\infty} -i*x*\Psi*e^{-i*k*x}*dk} $$
-;$$ \frac{\partial \psi}{\partial k} = \circlearrowleft(-90\degree)*F^{-1}(\Psi*k)\textcolor{red}{=-i*F^{-1}(\Psi*k)} $$
-
----
-
-### Impulsraum
-
$$ \psi = F(\Psi) = \int_{-\infty}^{\infty} \circlearrowleft(-k*x)*\Psi*dx \textcolor{red}{=\int_{-\infty}^{\infty}
\Psi*e^{-i*k*x}*dk}$$
diff --git a/src/python/oscillator.py b/src/python/oscillator.py
index c2885de..e99ccfd 100644
--- a/src/python/oscillator.py
+++ b/src/python/oscillator.py
@@ -63,4 +63,20 @@
ani = animation.FuncAnimation(
fig, animate, interval=1000/framerate, blit=True, save_count = framerate * totalTime)
ani.save(f"{outputFolder}oscillator.mp4")
-plt.show()
+
+fig, diagrammAx = plt.subplots()
+
+diagrammAx.axis("equal")
+diagrammAx.set_ylim(-1.5*A, 1.5*A)
+diagrammAx.set_xlim(-1.5*A, 1.5*A)
+diagrammAx.set_xlabel("x")
+diagrammGraph, = diagrammAx.plot([0, 1], [0, 0], "o-")
+
+def animate(i):
+ t = i/framerate
+ x = position(t)
+ diagrammGraph.set_data([0, x], [0, 0])
+ return diagrammGraph,
+ani = animation.FuncAnimation(
+ fig, animate, interval=1000/framerate, blit=True, save_count = framerate * totalTime)
+ani.save(f"{outputFolder}oscillator_simple.mp4")
diff --git a/src/python/photon.py b/src/python/photon.py
index eb6a715..632f808 100644
--- a/src/python/photon.py
+++ b/src/python/photon.py
@@ -4,7 +4,7 @@
outputFolder = "src/static/video/"
-totalTime = 12
+totalTime = 4 * 2 / 3
framerate = 20
psi = lambda x,t,n: np.sin(n*np.pi*x) * np.exp(-0.25j*n**2*np.pi*t)