Question

If the solutions are quantum fileds, rather than wavefunctions, then A and B behave different mathematically. They are now non-commuting variables that satisfy the following:

A^*A+AA^* = n

B^*B+BB^* = m

A^*B-BA^* = 0

B*A-AB^* = 0

where n and m are quantum numbers, and n represents the number of particles present in the field, and m the number of anti-particls. For a general solution ψ=ψ₊ + ψ_- , show that the density of ρ given in problem below now equals the number of particles minus the number of anti-particles.

ρ = n - m

ρ = i [ψ^* (∂ψ/ ∂t) − ψ (∂ψ^*/ ∂t)]

Answer 1