Advanced Quantum Mechanics Summarized
This 90-minute lecture is my attempt of distilling a large amount of rather advanced concepts in quantum mechanics down to their essentials. By the end of it, you will have heard of various concepts and fields that are very important in modern physics and motivate you to study them in depth yourself.
Introduction
The state of a quantum system is expressed with the Ket-vector \(|\psi \rangle \in \mathcal{H}\) in the unitary space \(\mathcal{H}\). What matters is the direction. \(|\psi \rangle\) and \(|\psi' \rangle = c \cdot |\psi\rangle\) where \(c \in \mathcal{C}\) are equivalent. And in the following, \(\langle \psi | \psi \rangle = 1\).
Superpositions are possible: \(|\chi \rangle, |\xi\rangle \in \mathcal{H} \Rightarrow |\psi|\rangle = a \cdot |\chi\rangle + b \cdot |\xi\rangle \in \mathcal{H}.\)
Bra-vectors