Creation or destruction of particol in the state function

[spocchio]

Hi,
I've studied a bit nuclear physics, and
I don't get how the mathematics under the creation and destruction of particles is handled.
if shrodingher equation leads a state vector in the usual way Hpsi=ih d(psi)/dt
let's suppose I've N particles and psi=psi(q1...qn)
so, if a new particle is created...does it mean my psi become psi=psi(q1...qn+1) ??
how can a mathematical frame handles this process?

the question could be reformulated as:
what happen to the state function when a new particle is created?

 

[henry_m]

Ordinary quantum mechanics can only deal with definite numbers of particles, pretty much for exactly the reason you have described. If you have a system with only a finite number of degrees of freedom, you can't describe a variable number of particles.

The solution to the problem lies in quantum field theory. Here, you have an infinite number of degrees of freedom (finitely many for every point in space) so you can happily describe as many or as few particles as you like.

 

[Bill_K]

The Hilbert space has a one-particle space described by Ψ(q₁), a two-particle space described by Ψ(q₁, q₂), and so on. The creation and annihilation operators take you from one subspace to another.