Inner product and Dirac Notation | Quantum Mechanics | LetThereBeMath |

In this video we continue talking about eigenstates and discuss the inner product and bra-ket notation, more formally known as Dirac notation.

[RossMcgowanMaths]

Very pleased that I found this video. I am starting out my studies in quantum mechanics. I have a reasonable knowledge in vector algebra and the ideas of functions as vectors and using the inner product to derive fourier transforms and ideas of hermitian functions but only in an electrical engineering context. I know these ideas are the cornerstones of quantum mechanics but needed a HOOK or an open door that I could push on in order to gain entry to this subject. This video has so many of my missing pieces of a jigsaw, now I feel I can start to see a picture appearing. Very excited by thiis video series. I am sitting with pen and paper and taking notes from these videos. It seems that formal instruction misses out or does not properly emphasise some basics. For example, I struggled with the ideax of Fourier and Laplace until someone told me functions are vectors too, then it all started making sense. The same had happened here. States or outcomes are bases of a vector space and probability amplitudes are scalar coefficients and we get probability by forming inner product just as we do with finding scalar coefficient in a fourier series. A light has come on !!!! Thank you.

[TheJasontaylor]

Brillaint vid. Very helpful and looking forward to more quantum vids

[jatyamxx]

A question, if there’s any chance you’ll see it: how would you go about proving that two kets decomposed in the circular basis form an orthonormal basis?

[RossMcgowanMaths]

Also covered calculus of variations and touched on hamiltonians, I think I have most of the mathematical pre requisites to make a good go atbunderstanding this subject.