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*Principles of Quantum Mechanics*) Introduces Bra-Ket notation in the first chapter rather concisely. I understand the mathematical basis of the Bras and Kets, but what is the physical interpretation of them?

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I suppose I used the wrong word... What does it represent? and how?

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Of course if you wanted, I suppose you could use ket vectors for your usual 3-dimensional mechanics problems in which case [tex]\left|\alpha\right\rangle = \left(x\:y\:z\right)^{T}[/tex] could represent any physical vector quantity you like?

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Basically, the complex number <out|O|in> is the amplitude to start from state |in> and end up to state |out> *via* the operator O.

But mathematically, <V| is the dual form to vector |V>.

__edit__

Excellent choice of book. Keep up with it, it's worth. You'll need to wait a little bit. Later in (12) "The general physical interpretation"

But mathematically, <V| is the dual form to vector |V>.

Excellent choice of book. Keep up with it, it's worth. You'll need to wait a little bit. Later in (12) "The general physical interpretation"

We therefore make the general assumption that if the measurement of the observable f for the system in the state corresponding to |x> is made a large number of times, the average of all the results obtained will be <x|f|x>, provided |x> is normalized.

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