For nonrelativistic motion we may neglect the magnetic force and replace the expression for m ẍ by: x ¨ ¨ + ω ω 0 2 x ≈ ≈ e m E ≈ ≈ ∑ ∑ k λ λ 2 π π ℏ ℏ ω ω k V [ a k λ λ ( t ) + a k λ λ † † ( t ) ] e k λ λ