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Dirac Notation (Bra-Ket) | Understanding the Maths of Quantum Mechanics

In this video I start by making an analogy about our emotions as emotional states and continue to introduce a powerful and compact mathematical framework that makes it easier for physicists to work with quantum mechanics. This notation was introduced by Dirac and is also known as Bra-Ket notation. I start by introducing ket and bra vectors which are elements of the Hilbert space and then operators that act on these vectors to transform then. Finally I talk about Hermitian operators which are crucial in understanding observables in quantum mechanics and also expectation values of these observables that are measures of the observables in our real world. 00:00 An analogy to better understand (emotional states) 02:23 Please DON'T get carried away by this analogy! 02:58 Dirac notation (bra-ket) 03:15 ket 03:38 bra 04:14 inner product (scalar product) 06:26 outer product 07:26 operators (Hermitian operators and observables) 09:27 expectation value of observables