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## Main Question or Discussion Point

Does the [tex]\langle \phi \rangle[/tex] means [tex] \langle0|\phi|0\rangle[/tex]?

What does [tex]|\phi|[/tex] exactly mean?

What does [tex]|\phi|[/tex] exactly mean?

- Thread starter princeton118
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Does the [tex]\langle \phi \rangle[/tex] means [tex] \langle0|\phi|0\rangle[/tex]?

What does [tex]|\phi|[/tex] exactly mean?

What does [tex]|\phi|[/tex] exactly mean?

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I'd guess your other one should have a square in it in which case it would mean modulys squared or in other words the complex conjugate of phi times phi

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I think that probably all the notations you used mean different things:Does the [tex]\langle \phi \rangle[/tex] means [tex] \langle0|\phi|0\rangle[/tex]?

What does [tex]|\phi|[/tex] exactly mean?

DIRAC NOTATIONS:

1.|psi> is a ket that lives in a hilbert space, math speaking is a state vector wich belongs to a projective hilbert space, ie it is a ray.

2.If the hilbert space is separable, you get the complet. relation---> Sum|n><n|=1;

u can have also generalized basis such as the deltas for x and plane waves for p, and the Sum become an integral.

3.a.You have also <x|x'>=delta(x-x')

3.b. or for a separable basis <n|n'>=delta_nn' (the last delta is a kronecker one).

4.Importamt <x|psi>=psi(x) and it is a complex function psi:R^3----->C

the wave function!

Now you can get the meaning of |psi|= the modulus of the wave function, while for the first notation <phi>=<0|phi|0> you have 2 choices i think:

a) it is a second quantization formalism, wich mean the vacuum expactation value of a field.

b)Or, if phi is an observable (P,H,L...), it can be the average over the ground state...

ususally when you start reading a book the conventions are displayed..

hope that helped..

marco

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