Inner Products | Pivotal Math of Quantum Mechanics | Quantum Theory

Join my Patreon community:   / abidebyreason   This is the third video in my Quantum Theory playlist. I explain what the inner product is in the context of Quantum Mechanics. I do this by reviewing what the dot product is and showing how the inner product is a generalization of it. 0:00 Introduction 0:49 Review of the Dot Product 1:05 Algebraic Definition of the Dot Product 1:24 Geometric Definition of the Dot Product 2:24 Relation between Dot Product and Angles/Lengths of Vectors 3:09 Motivation of Inner Product in Quantum Mechanics 4:57 The 4 Rules an Inner Product Must Satisfy (Definition) 6:33 Conclusion Related Videos: The Stern-Gerlach Experiment:    • Know This, If You Want to Understand Quant...   Why John Bell Deserved a Nobel Prize:    • Bell's Theorem Clearly Explained | Quantum...   How Bra Ket Notation Works:    • Don't blindly apply, UNDERSTAND Bra Ket No...   Schrödinger's Uncertainty Principle & its Relation to Heisenberg's:    • How Schrödinger Improved the Heisenberg U...   Maccone-Pati Uncertainty Relations:    • The Quantum Triviality Problem Schrödinge...   Quantum Theory Playlist:    • Quantum Theory