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Videos on momentum operator generating translations in quantum mechanics:
Physics with Elliot: • The Symmetry at the Heart of the Cano...
Professor M Does Science's video: • The translation operator in quantum m...
Quantum Sense': • Ch 14: Where does the momentum operat...
0:00 Introduction
2:45 Groups & Lie Groups
4:00 Exponent of a so(3) Matrix
7:40 Calculating so(3) generators
9:50 Momentum generators translations
10:58 so(3) traceless proof
13:35 so(3) antisymmetric proof
15:11 Warning about matrix exponentials
16:43 Lie Algebra Bracket
20:24 Structure coefficients
21:48 Lie Algebras as Tangent Spaces
23:30 Lie Algebra Property Proofs
30:15 Summary of so(3)
31:05 Overview of so+(1,3)
32:50 Spin1 and Spin1/2 representations
34:40 Math vs Physics conventions