diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json
index ee1c149..366131a 100644
--- a/.obsidian/workspace.json
+++ b/.obsidian/workspace.json
@@ -216,6 +216,8 @@
   },
   "active": "25f5b25d5eca7203",
   "lastOpenFiles": [
+    "SS2026/Quantum Computing/4. Observing and measuring/Anhänge/Pasted image 20260729101220.png",
+    "SS2026/Quantum Computing/4. Observing and measuring/Anhänge/Pasted image 20260729101158.png",
     "SS2026/Quantum Computing/4. Observing and measuring/Anhänge/Pasted image 20260729100435.png",
     "SS2026/Quantum Computing/4. Observing and measuring/Anhänge/Pasted image 20260729100407.png",
     "SS2026/Quantum Computing/4. Observing and measuring/Anhänge/Pasted image 20260729094718.png",
@@ -229,8 +231,6 @@
     "SS2026/Quantum Computing/4. Observing and measuring/Observing probabilistic and measuring quantum systems.md",
     "SS2026/Quantum Computing/4. Observing and measuring",
     "SS2026/Quantum Computing/3. Quantum Systems/Anhänge/Pasted image 20260729092121.png",
-    "SS2026/Quantum Computing/3. Quantum Systems/Anhänge/Pasted image 20260729092010.png",
-    "SS2026/Quantum Computing/3. Quantum Systems/Anhänge/Pasted image 20260729091741.png",
     "SS2026/Quantum Computing/3. Quantum Systems/Anhänge",
     "SS2026/Quantum Computing/2. Probabilistic systems/Probabilistic Systems.md",
     "SS2026/Quantum Computing/3. Quantum Systems",
diff --git a/SS2026/Quantum Computing/4. Observing and measuring/Anhänge/Pasted image 20260729101158.png b/SS2026/Quantum Computing/4. Observing and measuring/Anhänge/Pasted image 20260729101158.png
new file mode 100644
index 0000000..3094937
Binary files /dev/null and b/SS2026/Quantum Computing/4. Observing and measuring/Anhänge/Pasted image 20260729101158.png differ
diff --git a/SS2026/Quantum Computing/4. Observing and measuring/Anhänge/Pasted image 20260729101220.png b/SS2026/Quantum Computing/4. Observing and measuring/Anhänge/Pasted image 20260729101220.png
new file mode 100644
index 0000000..c0e3880
Binary files /dev/null and b/SS2026/Quantum Computing/4. Observing and measuring/Anhänge/Pasted image 20260729101220.png differ
diff --git a/SS2026/Quantum Computing/4. Observing and measuring/Observing probabilistic and measuring quantum systems.md b/SS2026/Quantum Computing/4. Observing and measuring/Observing probabilistic and measuring quantum systems.md
index 754c311..b5f5994 100644
--- a/SS2026/Quantum Computing/4. Observing and measuring/Observing probabilistic and measuring quantum systems.md	
+++ b/SS2026/Quantum Computing/4. Observing and measuring/Observing probabilistic and measuring quantum systems.md	
@@ -38,4 +38,16 @@ To test, a photon can be send through the box.
 
 A beam splitter is a semi transparent mirror.
 Photons entering from up can come out on the up or down path - analog for down
-Quantum mechanically it could come in a superposition between up and down
\ No newline at end of file
+Quantum mechanically it could come in a superposition between up and down
+$\begin{pmatrix} \alpha \\ \beta \end{pmatrix}$ a = amplitude of up, b = amplitude of down
+And it would exit the beam splitter in a superposition between up and down again
+$\begin{pmatrix} \gamma \\ \delta \end{pmatrix}$ gamma = up, delta = down
+
+![[Pasted image 20260729101158.png]]
+
+The bomb tester now looks like this:
+
+![[Pasted image 20260729101220.png]]
+
+
+