Quantum Mechanics: Learning Bra-Ket Notation

[Reedeegi]

I began my physics study about one year ago and learned all of classical mechanics in that year; but I am now studying Quantum Mechanics. The book I'm using (Dirac's 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?

 

[K.J.Healey]

Its a representation. Why does it need a physical meaning? Maybe a wavefunction, if you consider that physical.

 

[Reedeegi]

Its a representation. Why does it need a physical meaning? Maybe a wavefunction, if you consider that physical.

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

 

[tshafer]

A ket vector describes a system in state space but, like so many things in quantum mechanics, I'm not sure you could attach a 'physical interpretation' to them.

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

 

[humanino]

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"

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.