Linear superposition of single-particle states

  • Thread starter Neitrino
  • Start date
134
0

Main Question or Discussion Point

Dear all,

I am not sure whether I understand correctly or not.
So from Peskin Schroeder’s book:
[tex]\phi(x)|0>=
\int{\frac{d^3 p}{(2\pi)^3}\frac{1}{2E_p}e^{-ipx}|p>
[/tex]
formula (2.41). Interpreting this formula they say – it’s a linear superposition of single-particle states that have well defined momentum. And also that operator phi(x) acting on the vacuum, creates a particle at position x.
My question – since it is a superposition of single-particle states and creates a particle at position X, So that operator creates many single-particle states with different momentum (since there is integration over p and each single-particle state has different momentum) and all of them (particles with different momentum ) are created at one position X?
Or briefly – many different momentum particles are created at one position X?

Thanks
 
Last edited:

Answers and Replies

vanesch
Staff Emeritus
Science Advisor
Gold Member
5,007
16
Neitrino said:
My question – since it is a superposition of single-particle states and creates a particle at position X, So that operator creates many single-particle states with different momentum (since there is integration over p and each single-particle state has different momentum) and all of them (particles with different momentum ) are created at one position X?
Or briefly – many different momentum particles are created at one position X?
What's the superposition of a one-particle and a one-particle state ? A two-particle state or another one-particle state ? Answer: another one-particle state. Superpositions of N-particle states are again N-particle states.
So you should view this as ONE particle is created, in a superposition of momentum states, exactly as in NR quantum mechanics, where ONE position state is written as (about the same) superposition of several momentum states.

cheers,
Patrick.
 

Related Threads for: Linear superposition of single-particle states

  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
1
Views
679
  • Last Post
Replies
8
Views
8K
Replies
6
Views
1K
Replies
24
Views
2K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
1
Views
607
Replies
1
Views
2K
Top