This commit is contained in:
2026-01-22 16:24:29 +01:00
parent 452cc87a57
commit a699022812
9 changed files with 973 additions and 14 deletions

1
autotodo/.gitignore vendored Normal file
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target

346
autotodo/Cargo.lock generated Normal file
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9
autotodo/Cargo.toml Normal file
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[package]
name = "autotodo"
version = "0.1.0"
edition = "2024"
[dependencies]
chrono = { version = "0.4.43", features = ["serde"] }
ron = "0.12.0"
serde = { version = "1.0.228", features = ["derive"] }

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@@ -0,0 +1,16 @@
[
(
name: "Rechnung Gertrudenhof",
pattern: Monthly(dom: 1),
),
(
name: "Rechnung STG",
pattern: MonthlyOpt(dom: 1, months: [February, May, August, November]),
),
(
name: "Kalender durchlesen",
pattern: Weekly(dow: 1),
),
]

33
autotodo/src/main.rs Normal file
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@@ -0,0 +1,33 @@
use std::fs;
use ron;
use serde::{Serialize, Deserialize};
use chrono;
#[derive(Serialize, Deserialize, Debug)]
enum Pattern {
Yearly { doy: u32 },
MonthlyOpt { dom: u32, months: Vec<chrono::Month> },
Monthly { dom: u32 },
Weekly { dow: u32 },
Daily,
}
#[derive(Serialize, Deserialize, Debug)]
struct Position {
name: String,
pattern: Pattern
}
fn parse_patterns() {
let f = fs::read_to_string("data/patterns.ron").expect("file should exist");
let patterns: Vec<Position> = ron::from_str(&f).expect("file should follow proper ron syntax");
dbg!(patterns);
}
fn parse_notes() {
}
fn main() {
parse_patterns();
}

139
bezier.py Normal file
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import matplotlib.pyplot as plt
import matplotlib.animation as animation
import math
import numpy as np
def binom(n,k):
return math.factorial(n) / (math.factorial(k) * math.factorial(n - k))
def bernstein(n,t):
return [binom(n,i) * t**i * (1-t)**(n-i) for i in range(n + 1)]
def d(x1,x2,y1,y2):
return ( (x2 - x1)**2 + (y2 - y1)**2 )**0.5
data_raw = [
[235.00,575.00], [233.17,556.00], [233.17,556.00],
[233.17,556.00], [231.00,527.00], [231.00,527.00],
[231.00,527.00], [230.00,511.00], [230.00,511.00],
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[1212.37,367.54], [1219.67,365.79], [1223.81,368.40],
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[1375.36,444.16], [1379.24,436.87], [1383.56,439.28],
[1388.01,441.76], [1381.78,454.41], [1380.42,458.00],
[1380.42,458.00], [1357.72,515.00], [1357.72,515.00],
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[1260.29,685.00], [1227.58,726.00], [1227.58,726.00],
[1221.64,732.97], [1214.42,739.11], [1215.10,749.00],
[1215.53,755.32], [1221.42,767.85], [1224.14,774.00],
[1235.06,798.70], [1251.02,819.02], [1270.00,838.00],
[1270.00,838.00], [1293.99,859.20], [1293.99,859.20],
[1297.51,862.12], [1302.08,865.88], [1301.51,871.00],
[1301.04,875.17], [1296.56,880.76], [1294.00,884.00],
[1294.00,884.00], [1276.00,906.00], [1276.00,906.00],
[1248.58,937.78], [1225.95,961.62], [1194.00,989.13],
[1094.90,1074.47], [971.72,1130.24], [842.00,1147.72],
[820.90,1150.56], [799.27,1152.97], [778.00,1153.00],
[778.00,1153.00], [761.00,1154.00], [761.00,1154.00],
[761.00,1154.00], [720.00,1153.00], [720.00,1153.00],
[720.00,1153.00], [710.00,1152.09], [710.00,1152.09],
[710.00,1152.09], [679.00,1149.72], [679.00,1149.72],
[672.74,1148.96], [657.43,1146.64], [652.00,1147.17],
[638.98,1148.45], [637.72,1151.92], [628.00,1155.91],
[620.06,1159.17], [610.56,1160.65], [602.00,1159.83],
[569.31,1156.71], [523.63,1143.05], [493.00,1130.80],
[418.51,1101.00], [346.38,1052.53], [287.00,998.83],
[253.81,968.81], [224.81,936.35], [197.42,901.00],
[197.42,901.00], [179.34,876.00], [179.34,876.00],
[176.97,872.48], [173.45,867.50], [174.35,863.00],
[175.36,857.98], [182.19,853.60], [186.00,850.55],
[192.40,845.43], [204.46,834.84], [209.91,829.00],
[222.15,815.87], [232.76,802.18], [242.32,787.00],
[242.32,787.00], [251.80,771.00], [251.80,771.00],
[252.93,769.08], [254.85,765.20], [256.49,763.93],
[258.42,762.45], [267.16,760.82], [270.00,760.21],
[270.00,760.21], [299.00,754.00], [299.00,754.00],
[247.20,699.70], [203.92,634.86], [168.31,569.00],
[168.31,569.00], [146.26,524.00], [146.26,524.00],
[146.26,524.00], [119.81,460.00], [119.81,460.00],
[118.69,457.06], [115.36,447.70], [115.01,445.00],
[114.71,442.72], [115.05,439.63], [118.07,439.63],
[121.71,439.63], [124.95,446.26], [126.68,449.00],
[126.68,449.00], [146.02,479.00], [146.02,479.00],
[163.90,504.93], [184.76,528.76], [207.00,551.00],
[213.14,557.14], [227.44,572.42], [235.00,575.00],
]
for p in data_raw:
p[0] = (p[0] - 750.0) / 1000.0
p[1] = (750.0 - p[1]) / 1000.0
x = []
y = []
for i in range(int((len(data_raw) - 1) / 3)):
idx = i * 3
# dis = d(data_raw[idx+1][0], data_raw[idx+4][0], data_raw[idx+1][1], data_raw[idx+4][1])
b1 = [data_raw[idx+i][0] for i in range(1,5)]
b2 = [data_raw[idx+i][1] for i in range(1,5)]
for t in np.linspace(0,1,200):
b = bernstein(len(b1) - 1, t)
x.append(sum([b[i] * b1[i] for i in range(len(b1))]))
y.append(sum([b[i] * b2[i] for i in range(len(b2))]))
proc_x = []
proc_y = []
for (re, im) in zip(x,y):
if len(proc_x) == 0 or d(re, proc_x[-1], im, proc_y[-1]) > 0.01:
proc_x.append(re)
proc_y.append(im)
print(proc_x)
print(proc_y)
print(len(proc_x))
plt.scatter(proc_x,proc_y)
# fig, ax = plt.subplots()
# ani = animation.FuncAnimation(fig=fig, func=update, frames=1000, interval=1)
plt.show()

View File

@@ -153,10 +153,10 @@ impl eframe::App for MyApp {
let trail_points: Vec<[f64;2]> = self.trail.iter().map(|p| p.1).collect(); let trail_points: Vec<[f64;2]> = self.trail.iter().map(|p| p.1).collect();
Plot::new("scatter_plot").show(ui, |plot_ui| { Plot::new("scatter_plot").show(ui, |plot_ui| {
// plot_ui.points(trail_scatter);
if !trail_points.is_empty() { if !trail_points.is_empty() {
for idx in 0..trail_points.len() - 1 { for idx in 0..trail_points.len() - 1 {
let alpha = (255.0 * (idx as f32) / trail_points.len() as f32).round() as u8; let alpha = 255 - ((time - self.trail[idx].0) / self.period * 255.0).round() as u8;
// let alpha = (255.0 * (idx as f32) / trail_points.len() as f32).round() as u8;
plot_ui.add(Line::new("trace", vec![trail_points[idx], trail_points[idx+1]]).width(2.0).color(Color32::from_rgba_unmultiplied(240, 100, 100, alpha))); plot_ui.add(Line::new("trace", vec![trail_points[idx], trail_points[idx+1]]).width(2.0).color(Color32::from_rgba_unmultiplied(240, 100, 100, alpha)));
} }

399
notes.md
View File

@@ -3,6 +3,8 @@ i: into issue
d: someone else did it / took "assignment" (spiritual or actually in Gitea) d: someone else did it / took "assignment" (spiritual or actually in Gitea)
r: tried unsucessfully, have to retry r: tried unsucessfully, have to retry
m: moved to a later, specified time m: moved to a later, specified time
c: i will come back to this when i feel like it, but no need to track it now
p: Made progress, but not done
# 2025-11-18 # 2025-11-18
@@ -453,7 +455,7 @@ m: moved to a later, specified time
# 2025-12-19 # 2025-12-19
- [x] Thomas 10 Uhr - [x] Thomas 10 Uhr
- [ ] GTH Doc anpassen - [ ] masterdoc anpassen
- [x] "Auszug unserer Referenzen" - [x] "Auszug unserer Referenzen"
- [x] pandaloop.de - [x] pandaloop.de
- [x] Smarter Einstieg Header über Console - [x] Smarter Einstieg Header über Console
@@ -494,7 +496,7 @@ m: moved to a later, specified time
# 2025-12-22 # 2025-12-22
- [r] GTH Doc anpassen - [r] masterdoc anpassen
- [r] Abbinder wir freuen uns + Gimmick - [r] Abbinder wir freuen uns + Gimmick
- [r] Cloud zu Business Software - [r] Cloud zu Business Software
- [r] Luftiger (3 Seiten) - [r] Luftiger (3 Seiten)
@@ -545,14 +547,387 @@ m: moved to a later, specified time
- [ ] Change Handelsregister (Notar does this) - [ ] Change Handelsregister (Notar does this)
- [ ] NEXT DOOR in Person besichtigen (bis Ende des Jahres) - [ ] NEXT DOOR in Person besichtigen (bis Ende des Jahres)
## Hypelist # 2025-12-23
- Aqualand - [x] Physik
- Remagen - [r] GTH Doc anpassen
- Netcologne - [r] Abbinder wir freuen uns + Gimmick
- GTH HA - [r] Cloud zu Business Software
- GTH Odoo - [r] Luftiger (3 Seiten)
- Justfit Next Door - [ ] CTA noch mehr inhaltlich (sprechen gut, aber auch inhaltlich ("transformieren" oder so))
- Adbelt - [ ] backslash in hallo@pandaloop.de
- Schokoladenmuseum - [ ] Tool-Übersicht (Software die wir einsetzen können (Odoo, HA, Rust, MikroTik))
- Intratone - [ ] Proposal Dokument touch ups
- [x] Buch abholen
- [ ] Wann Deadline für unsere privaten Steuererklärungen
- [ ] Wojtek
- [ ] Cow hours bugs (pre und post runden)
- [ ] Nextcloud aufräumen
- [ ] Island: Cloud Produkt zu Business Software Produkt
- [ ] Anh-Tuan schreiben
- [ ] Kreditbedingungen Wojtek herausfinden?
- [ ] Sehtest / Brille
- [ ] Wojtek & R1
- [ ] Termin vereinbaren
- [ ] Hold GSV for Wojteks end at PL
- [ ] Hold notary appointment for both Anteilskauf and GF-Abberufung
- [ ] Change Handelsregister (Notar does this)
- [ ] NEXT DOOR in Person besichtigen (bis Ende des Jahres)
# 2025-12-29
- [x] Proposal Dokument touch ups
- [r] masterdoc anpassen
- [r] Abbinder wir freuen uns + Gimmick
- [r] Cloud zu Business Software
- [r] Luftiger (3 Seiten)
- [ ] CTA noch mehr inhaltlich (sprechen gut, aber auch inhaltlich ("transformieren" oder so))
- [ ] backslash in hallo@pandaloop.de
- [ ] Tool-Übersicht (Software die wir einsetzen können (Odoo, HA, Rust, MikroTik))
- [x] Wann Deadline für unsere privaten Steuererklärungen -> 30.04.2026
- [x] Wojtek anschreiben
- [x] Januar Üebrlegungen mit Hassan
- [x] Aqualand
- [x] Remagen
- [x] Netcologne
- [x] GTH HA
- [x] GTH Odoo
- [x] Justfit Next Door
- [x] Adbelt
- [x] Schokoladenmuseum
- [x] Intratone
- [ ] Cow hours bugs (pre und post runden)
- [ ] Nextcloud aufräumen
- [ ] Island: Cloud Produkt zu Business Software Produkt
- [x] Anh-Tuan schreiben
- [ ] Kreditbedingungen Wojtek herausfinden?
- [ ] Sehtest / Brille
- [ ] Wojtek & R1
- [ ] Termin vereinbaren
- [ ] Hold GSV for Wojteks end at PL
- [ ] Hold notary appointment for both Anteilskauf and GF-Abberufung
- [ ] Change Handelsregister (Notar does this)
- [ ] NEXT DOOR in Person besichtigen (bis 06.01.)
# 2026-01-02
- [r] masterdoc anpassen
- [r] Abbinder wir freuen uns + Gimmick
- [r] Cloud zu Business Software
- [r] Luftiger (3 Seiten)
- [ ] CTA noch mehr inhaltlich (sprechen gut, aber auch inhaltlich ("transformieren" oder so))
- [ ] backslash in hallo@pandaloop.de
- [ ] Tool-Übersicht (Software die wir einsetzen können (Odoo, HA, Rust, MikroTik))
- [ ] Rechnung GTH
- [ ] Rechnung Tim + Report
- [ ] ICDSA angucken
- [ ] Graphite angucken
- [n] Cow hours bugs (pre und post runden)
- [ ] Nextcloud aufräumen
- [ ] Island: Cloud Produkt zu Business Software Produkt
- [ ] Kreditbedingungen Wojtek herausfinden?
- [ ] Sehtest / Brille
- [ ] Wojtek & R1
- [ ] Termin vereinbaren
- [ ] Hold GSV for Wojteks end at PL
- [ ] Hold notary appointment for both Anteilskauf and GF-Abberufung
- [ ] Change Handelsregister (Notar does this)
- [ ] NEXT DOOR in Person besichtigen (bis 06.01.)
# 2026-01-05
- [x] masterdoc anpassen
- [x] Abbinder wir freuen uns + Gimmick
- [x] Cloud zu Business Software
- [x] Luftiger (3 Seiten)
- [x] CTA noch mehr inhaltlich (sprechen gut, aber auch inhaltlich ("transformieren" oder so))
- [x] backslash in hallo@pandaloop.de
- [x] Tool-Übersicht (Software die wir einsetzen können (Odoo, HA, Rust, MikroTik))
- [x] Rechnung GTH
- [x] Rechnung Tim + Report
- [r] Bundesanzeiger Unstimmigkeitsmeldung
- [ ] Physik
- [x] Island: Cloud Produkt zu Business Software Produkt
- [ ] ICDSA angucken
- [ ] Graphite angucken
- [ ] Nextcloud aufräumen
- [ ] Sehtest / Brille
- [ ] NEXT DOOR in Person besichtigen
- [ ] Wojtek & R1
- [ ] Kreditbedingungen herausfinden
- [ ] Termin vereinbaren
- [ ] Hold GSV for Wojteks end at PL
- [ ] Hold notary appointment for both Anteilskauf and GF-Abberufung
- [ ] Change Handelsregister (Notar does this)
# 2026-01-06
- [x] Tim antworten
- [ ] Bundesanzeiger Unstimmigkeitsmeldung
- [x] Thomas Meeting
- [x] Erster Text griffiger / expliziter "Was machen wir anders / besonders:" ("zuverlässig", "verlässlich", "schnell", "allumfassend")
- [x] Kundenzitat
- [n] Schnelle Auffassungsgabe
- [x] "kurz gesagt: Egal was dein IT-Problem ist, wir können helfen."
- [x] "Ich habe nicht geglaubt, dass die eierlegende Wollmilchsau wirklich existiert. Pandaloop hat mich eines besseren belehrt."
- [x] Griffiger, Mehr Arroganz, knapper, evtl. Kundenstimme, schon noch kurze Antwort auf "Was" drin haben
- [x] CTA: "Lassen Sie uns über Ihre IT sprechen."
- [c] Website: auch ein CTA
- [c] Website: Interaktive Elemente (Bot, In Kontakt treten, Preis-Rechner)
- [ ] Website: Thomas auf Website
- [x] Kübra antworten (UstIDNr Meldung)
- [ ] Thomas Mail Feedback
- [ ] Physik
- [ ] ICDSA angucken
- [ ] Graphite angucken
- [ ] Nextcloud aufräumen
- [ ] Sehtest / Brille
- [ ] NEXT DOOR in Person besichtigen
- [ ] Wojtek & R1
- [ ] Kreditbedingungen herausfinden
- [ ] Termin vereinbaren
- [ ] Hold GSV for Wojteks end at PL
- [ ] Hold notary appointment for both Anteilskauf and GF-Abberufung
- [ ] Change Handelsregister (Notar does this)
# 2026-01-07
- [x] Bundesanzeiger Unstimmigkeitsmeldung -> mal schauen obs funktioniert
- [ ] Anh-Tuan
- [p] Netcologne Doc -> Draft
- [ ] Bob
- [ ] Physik
- [ ] ICDSA angucken
- [ ] Graphite angucken
- [ ] Nextcloud aufräumen
- [ ] Sehtest / Brille
- [ ] NEXT DOOR in Person besichtigen
- [ ] Wojtek & R1
- [ ] Kreditbedingungen herausfinden
- [ ] Termin vereinbaren
- [ ] Hold GSV for Wojteks end at PL
- [ ] Hold notary appointment for both Anteilskauf and GF-Abberufung
- [ ] Change Handelsregister (Notar does this)
# 2026-01-08
- [ ] Physik
- [x] Bell Theorem
- [ ] Lernplan
- [ ] Anh-Tuan
- [ ] Netcologne Doc
- [ ] Bob
- [x] Aqualand Thomas
- [x] Spotify Player
- [x] Essen
- [x] Zoggen
- [ ] DnD Character
- [ ] NEXT DOOR in Person besichtigen
- [c] ICDSA angucken
- [c] Graphite angucken
- [c] Nextcloud aufräumen
- [c] Sehtest / Brille
- [ ] Wojtek & R1
- [ ] Kreditbedingungen herausfinden
- [ ] Termin vereinbaren
- [ ] Hold GSV for Wojteks end at PL
- [ ] Hold notary appointment for both Anteilskauf and GF-Abberufung
- [ ] Change Handelsregister (Notar does this)
# 2026-01-09
- [ ] Physik
- [ ] Lernplan (GT, Prüfungen, P5, Recr)
- [ ] GT
- [ ] Anh-Tuan
- [ ] Netcologne Doc
- [ ] Bob
- [ ] DnD Character
- [ ] Wojtek & R1
- [ ] Kreditbedingungen herausfinden
- [ ] Termin vereinbaren
- [ ] Hold GSV for Wojteks end at PL
- [ ] Hold notary appointment for both Anteilskauf and GF-Abberufung
- [ ] Change Handelsregister (Notar does this)
# 2026-01-12
- [ ] Schild "keine Werbung"
- [ ] Aufräumen organisieren?
- [ ] Physik
- [ ] Lernplan (GT, Prüfungen, P5, Recr)
- [ ] GT
- [ ] Anh-Tuan
- [ ] Netcologne Doc
- [ ] Bob
- [ ] DnD Character
- [ ] Wojtek & R1
- [ ] Kreditbedingungen herausfinden
- [ ] Termin vereinbaren
- [ ] Hold GSV for Wojteks end at PL
- [ ] Hold notary appointment for both Anteilskauf and GF-Abberufung
- [ ] Change Handelsregister (Notar does this)
# 2026-01-13
- [ ] Mika Attest
- [ ] Corni Brief
- [p] Netcologne Doc
- [ ] Akquise
- [ ] Schild "keine Werbung"
- [ ] Aufräumen organisieren?
- [ ] Physik
- [ ] Bob
- [ ] Wojtek & R1
- [ ] Kreditbedingungen herausfinden
- [ ] Termin vereinbaren
- [ ] Hold GSV for Wojteks end at PL
- [ ] Hold notary appointment for both Anteilskauf and GF-Abberufung
- [ ] Change Handelsregister (Notar does this)
# 2026-01-14
- [ ] Mika Attest
- [x] Netcologne Doc
- [ ] Schild "keine Werbung"
- [ ] Aufräumen organisieren?
- [ ] Physik
- [ ] Bob
- [ ] Wojtek & R1
- [ ] Kreditbedingungen herausfinden
- [ ] Termin vereinbaren
- [ ] Hold GSV for Wojteks end at PL
- [ ] Hold notary appointment for both Anteilskauf and GF-Abberufung
- [ ] Change Handelsregister (Notar does this)
- [ ] E-Feld bei Kabeln
- [ ] Retardiertes Feld
# 2026-01-15
- [x] Pit Doc
- [ ] Akquise
- [ ] Physik
- [x] Jörg?
- [r] Uli?
- [ ] Wojtek?
- [x] Schild "Pandaloop" & "keine Werbung"
- [ ] Aufräumen organisieren?
- [ ] Bob
- [ ] Wojtek & R1
- [ ] Kreditbedingungen herausfinden
- [ ] Termin vereinbaren
- [ ] Hold GSV for Wojteks end at PL
- [ ] Hold notary appointment for both Anteilskauf and GF-Abberufung
- [ ] Change Handelsregister (Notar does this)
# 2026-01-16
- [ ] CRM updaten
- [x] Morello Code aktualisieren
- [x] Thomas Überweisung
- [ ] AWH
- [ ] Physik
- [ ] Aufräumen organisieren?
- [ ] Bob
- [ ] Wojtek & R1
- [ ] Termin vereinbaren
- [ ] Hold GSV for Wojteks end at PL
- [ ] Hold notary appointment for both Anteilskauf and GF-Abberufung
- [ ] Change Handelsregister (Notar does this)
# 2026-01-19
- [x] Remagen Meeting
- KI im Verkauf
- Prompting Fortbildung?
- Altlast abschaffen
- Herr Hammel
- Noch mehr Programme
- CSB wird mit IDs aufgerufen?
- unsere Aufgabe: Strukturiert zusammentragen
- 250 Mitarbeiter
- 2010:27M, Heute: 82M
- Digitalisierung ist das Hauptziel
- Beide ERPs benutzen
- Prozesse simulieren
- Alles kg
- Scanner bekommt keine EDI-Infos?
- Playbooks schreiben
- Rechte Hände vom Bollig
- Machines in ...GLT?
- Manuell oder händisch scannen
- Wareneingang, EK, Nummernkreise
- Haupteingang
- Morgen Aufgaben: 1. Realprozesse verstehen 2. Interaktionen mit System verstehen 3. Aufbau der Datensätze verstehen 4. Änderungsbedarfe an Datensätzen aufnehmen
Aktuelle Projekte:
- Odoo / Orion
- Bob
- Leads (Remagen)
- [r] Bob
- [x] GTH Doc einen Punkt adden (Hassan)
- [ ] Physik
- [x] CRM updaten
- [x] Bescheid geben wegen meiner Akquise
- [x] Bisschen Überblick bekommen (STG Rechnung zb hatte ich irgendwie nicht aufm Schirm)
- [ ] Solti Vertrag?
- [ ] ToDo-Automatisierungsprogramm?
- [ ] Neues Morello Programm?
- [ ] Wojtek & R1
- [ ] Termin vereinbaren
- [ ] Hold GSV for Wojteks end at PL
- [ ] Hold notary appointment for both Anteilskauf and GF-Abberufung
- [ ] Change Handelsregister (Notar does this)
# 2026-01-22
- [x] Thmomas meeting
- Außendarstellung: Nach Feedback fragen
- Yncoris als Projektarbeit
- Yncoris schon Termin?
- [x] Thomas Termin schicken Netcologne
- [x] Cow hours
- [x] Hassan Gespräch mit Elmar (bevor ihr die erste Rechnung schickt...) -> Nochmal Bedürfnisse klären (Stundenzettel, Eigenständigkeit, Rosa-Äquivalent)
- [x] Martin Termin shcicken
- [ ] Remagen
- [ ] Vertrag
- [ ] Stundendoc
- [ ] Repo
- [ ] Bob
- [ ] Physik
- [ ] Orion
- [ ] Vertrag
- [ ] Rechnung über Odoo / 12
- [ ] ToDo-Automatisierungsprogramm?
- [ ] Neues Morello Programm?
- [ ] Wojtek & R1
- [ ] Termin vereinbaren
- [ ] Hold GSV for Wojteks end at PL
- [ ] Hold notary appointment for both Anteilskauf and GF-Abberufung
- [ ] Change Handelsregister (Notar does this)

40
physics.md Normal file
View File

@@ -0,0 +1,40 @@
# Group Theory
## Basics
- Representation: p: G -> GL(V), a map from the group the set of linear maps from V to V (ambigous if Representation means the map p or the resulting set of linear maps)
- Lie Algebra: Vector space + inner product (vector product) that is bilinear, follows the jacobi identity, and has x*x = 0
## Wigner D/d-matrix (sheet 07) -> Dive into angular momentum maths
- Generator operators U(R) = exp(-ihJ), J: operator / infinitesimal rotation
- SO(3) has exactly one irrep of dim 1,3,5,... (=2j+1) -> How does this relate to number of eigenstates?
- SU(2) allows even dim as well (j = half-integer) because SU(2) is double cover of SO(3) -> research
- Wigner D-Matrix gives transition probabilities between eigenstates
- Eigenstates form basis when discrete
- When j= 3, m=-3,-2,-1,0,1,2,3 -> states |3m> are allowed -> real states are superpositions of these basis states / eigenstates -> 7-dim space needed to describe them (even though angular momentum needs only 3d classically) -> remember in general that degrees of freedom explode as 2^n because superpositions are allowed
- j fixes total angular momentum, m fixes z component
- angular momentum operator algebra is inherent to so(3) lie algebra
## Questions / open things
- Where does the inherent need for SO(3) come from? Why are the possible state spaces the irreps of SO(3)?
-> The operators that rotate states (in physical space) can be called U(R(theta)), where R in SO(3). There is a homomorphism between {U(R)} and SO(3), since U(R1R2)=U(R1)U(R2). Thus U(R) is a representation.
Enforcing finite-dim and irrep, this fixes dim = 2j+1.
- What about that L/J algebra? See "Lie Algebra" german wikipedia article -> Beispiele -> Aus der Physik -> Seems as though the relation does not only hold for those three "basis matrices", but all matrices, as long as your in the basis of the L_i (wtf even is a basis of matrices)
- Is there an intuitive notion to see how angular momentum emerges from the shapes of the wave functions?
- How does the emergence of azimuthal dependence in superpositions of (not azimuth-constraining) eigenstates play out mathematically?
- Why is SU(2) the double cover of SO(3)? What does that mean?
- What role do Pauli matrices play (generators of SO(2)? idk)
- How does one come up with the idea that operators and eigenvalues/vectors are the appropriate mathematical tools to describe QM? How does it arise? BC this alone imposes a lot of the quantization maths, since eigenvalues are discrete
- relation between Lie algebras and Lie groups not exactly clear
- Whats the algebra of exp of matrices -> https://de.wikipedia.org/wiki/Matrixexponential
- Is the generator exp(-ihJ) for SO(3) just the most convinient choice or the only choice?
## Next topics
- Character tables and relation between conjugacy classes and irreps
- Further sheets
- Further lectures, explicitly everything after lecture 09
- Wigner-Eckart Theorem (in lecture, sheet and indip research)
- Clebsch Gordan coeff as seperate research?