Question about the notation in Quantum Physics

[princeton118]

Does the \langle \phi \rangle means \langle0|\phi|0\rangle?
What does |\phi| exactly mean?

 

[CPL.Luke]

<B> means <y|B|y> where y is some given wavefunction.

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

 

[Marco_84]

Does the \langle \phi \rangle means \langle0|\phi|0\rangle?
What does |\phi| exactly mean?

I think that probably all the notations you used mean different things:

DIRAC NOTATIONS:

1.|psi> is a ket that lives in a hilbert space, math speaking is a state vector which 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, which 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