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Linear superposition of singleparticle states 
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#1
Sep205, 09:28 AM

P: 133

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 singleparticle 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 singleparticle states and creates a particle at position X, So that operator creates many singleparticle states with different momentum (since there is integration over p and each singleparticle 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 


#2
Sep205, 01:57 PM

Emeritus
Sci Advisor
PF Gold
P: 6,236

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. 


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