PSA: My first name is Dillon, my last name is Berger. In Quantum Mechanics the initial state goes on the |right〉& the final state goes on the〈left|pic.twitter.com/0AplZO0UYZ
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Why is it written that way?
because we denote a vector as |v> , and we denote a vector that we wish to take the 'dot product' with as <v|
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Why are vectors denoted that way and not as a letter with a little arrow on top
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It has many advantages! Dual spaces, completeness for example. It gives way to a more intuitive understanding of more abstract ideas in linear algebra. If you look on my website I try to motivate this
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This is much less confusing if you note |v> denotes a vector in Hilbert space H, and <f| a functional in the dual vector space H^*, (i.e. |v> and <f| live in different spaces!). However, the innerproduct (, ) on H defines for every vector |v> a functional (|v>, --) denoted <v|.
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