This is a good explanation, but unfortunately it's wrong. You don't actually need to invoke quantization of light (i.e. photons) to derive the photoelectric effect, or multiphoton ionization.
You can actually use a semiclassical model - electrons are quantized, and obey the Schrodinger equation, but EM radiation is fully classical. I.e., just solve the time dependent Schrodigner equation with V(x,t) = V_{atom}(x) + cos(wt) E x.
Using this model, you derive exactly what the photonic theory intuitively predicts - i.e., the rate of 2-photon ionization scales like O(I^2) (i.e. probability of ionization = probability of 2 photons hitting simultaneously), n-photon ionization scales like O(I^n), etc.
Unfortunately I can only give paywalled references for this:
A. Jensen A. Galtbayar and K. Yajima. Local time-decay of solutions
to schrodinger equations with time-periodic potentials. J. Stat. Phys.,
116:231, 2004.
O. Costin, R. D. Costin, and J. L. Lebowitz. Time asymptotics of the
Schr¨odinger wave function in time-periodic potentials. J. Statist. Phys.,
116(1-4):283–310, 2004.
S Geltman. Multiphoton ionization of atoms. J. Phys. B: At. Mol. Phys.,
10:831, 1974.
R. V. Jensen and I.B. Bernstein. Semiclassical theory of relativistic electrons
in space and time varying electromagnetic field. Phys. Rev. A.,
29:282–289, 1984.
You can actually use a semiclassical model - electrons are quantized, and obey the Schrodinger equation, but EM radiation is fully classical. I.e., just solve the time dependent Schrodigner equation with V(x,t) = V_{atom}(x) + cos(wt) E x.
Using this model, you derive exactly what the photonic theory intuitively predicts - i.e., the rate of 2-photon ionization scales like O(I^2) (i.e. probability of ionization = probability of 2 photons hitting simultaneously), n-photon ionization scales like O(I^n), etc.
Unfortunately I can only give paywalled references for this:
A. Jensen A. Galtbayar and K. Yajima. Local time-decay of solutions to schrodinger equations with time-periodic potentials. J. Stat. Phys., 116:231, 2004.
O. Costin, R. D. Costin, and J. L. Lebowitz. Time asymptotics of the Schr¨odinger wave function in time-periodic potentials. J. Statist. Phys., 116(1-4):283–310, 2004.
S Geltman. Multiphoton ionization of atoms. J. Phys. B: At. Mol. Phys., 10:831, 1974.
R. V. Jensen and I.B. Bernstein. Semiclassical theory of relativistic electrons in space and time varying electromagnetic field. Phys. Rev. A., 29:282–289, 1984.