Timeline for Can everything in QM be described with degrees instead of matrices and vectors?

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Oct 18 '19 at 8:34 comment |x><y| * |z> = |x> * <y|z> = |x> * c (c is the inner product) = c|x>. Remember that the inner product can be though of as how much two states are similar. And order of multiplication doesn't matter when you multiply by a scalar.
Oct 18 '19 at 2:47 comment Can you explain this |x><y| * A = (how much y is simialar to A) * |x>
Oct 17 '19 at 18:33 comment Dirac is just a way to represent vectors. At the end of the day the rules for matrix multiplication applies. if you have a scalar 'a' and a matrix/vector V. then aV = Va. the result of an inner product is a scalar, so you can write it to the left/or right of the vector. If you have 2 operators(matrices) A,B and a state (vector) x, then AB|x> means that B is acting on x, and A is acting on the resulting vector. |0><1| is the col(1,0) * row(0,1) = 2x2 matrix: [[0,1],[0,0]]. I advise you to compute some outer products and act them on different states to get the intuition for what the do/mean
Oct 16 '19 at 4:51 comment "Yes, you calculate from right to left." Why from right to left??? I find this (|φ><ψ|)|y> = |φ>(<ψ|y>) and this |ω〉〈τ|(|ψ〉) = |ω〉〈τ|ψ〉 = 〈τ|ψ〉|ω〉, it looks like doesn't matter for right-left? Look same.
Oct 10 '19 at 2:40 comment -1) "|x><y|*A" how this become (<y|A)*|x> and not |x>(<y|*A) if "Yes, you calculate from right to left"? -2) Do you know any software for that "convert Dirac to matrices and vectors" and back?
Oct 9 '19 at 8:16 comment 1- Yes, you calculate from right to left. 2- X = X = |0><1| + |1><0|, |0><1| by it self is not unitary. 3- correct except the last statement. The inner product of "<y| * A" is a scalar (number). then the the state will be that scalar * |x> (not outer product). Finally, I suggest that, if you ever struggle with the dirac notation, just convert to matrices and vectors and do the multiplication. You'll get much better intuition of what's happening and why.
Oct 9 '19 at 6:52 history edited