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- Confused by manipulations within a sum using bra-ket notation (in a teaching video). The context is the expansion of a quantum state using an orthonormal basis.

I suspect it will help if you know about my background: I did some linear algebra in university but never used it and am now in my mid 60s. I am interested in understanding the mathematics of quantum physics. I have read a number of layman's texts on quantum mechanics, but they all gloss over the math.

I found this very interesting series online and I have a question about one of the videos that deals with "bras" and "bra-ket" notation; here is the link:

At the 8 minute mark, an example begins. At 8:25, he says "let's move the inner product to the front". While I think I understand the basics of inner products, I do not understand how such a move is justified or exactly what he is doing. It almost seems that he misspoke and should have said "let's move the inner product to the

I believe I understand the bit at 8:32 about "breaking the inner product apart", but I do not understand how the two Ai's together constitute an operator (although I believe I correctly understand what an operator is - it is a mathematical object that acts on a vector to generate another vector). Maybe it is the notation that is tripping me up.

Any words of wisdom greatly appreciated.

Reference: https://www.physicsforums.com/forums/linear-and-abstract-algebra.75/post-thread

I found this very interesting series online and I have a question about one of the videos that deals with "bras" and "bra-ket" notation; here is the link:

At the 8 minute mark, an example begins. At 8:25, he says "let's move the inner product to the front". While I think I understand the basics of inner products, I do not understand how such a move is justified or exactly what he is doing. It almost seems that he misspoke and should have said "let's move the inner product to the

**back**". Has he mis-spoken? Assuming he is not, what is going on at this point?I believe I understand the bit at 8:32 about "breaking the inner product apart", but I do not understand how the two Ai's together constitute an operator (although I believe I correctly understand what an operator is - it is a mathematical object that acts on a vector to generate another vector). Maybe it is the notation that is tripping me up.

Any words of wisdom greatly appreciated.

Reference: https://www.physicsforums.com/forums/linear-and-abstract-algebra.75/post-thread