Linearly polarized light of angular frequency w = kc is incident on a one-electron “atom" whose wave function can be app

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Linearly Polarized Light Of Angular Frequency W Kc Is Incident On A One Electron Atom Whose Wave Function Can Be App 1 (151.05 KiB) Viewed 62 times

Linearly polarized light of angular frequency w = kc is incident on a one-electron “atom" whose wave function can be approximated by the ground state of a 3D isotropic harmonic oscillator of angular frequency wn: 01(x) = (x1) = me 3/4 e-mynd/21 = th (a) Take the ejected electron of mass m to be in a plane-wave state of momentum Pj = hk 1 pi piky. = L3/2 Ej = 2m Starting from the expression for photon absoprtion (z/kg) = 2nch H(t) = 40 €.peika eiwt MC A. Vw13 show that the differential cross section for the cjection of an electron is given by do WA ap, L3 (kesleikite plo1 dΩ Nc/L3 2rhmw арі 27mwl al|0:912 where Nc/L is the flux of incoming photons, and P;(q) is the inverse Fourier transform of (a). (b) The coordinate system used is shown below, with k = kñ, and ê and ñ are the (linear) polarization and propagation directions of the photon, respectively. Evaluate the integral and show that the differential cross section given by 4ahkih h 002 exp ( TILLO [2hk x exp cos sin cos mw وندا V انمائي ru 3+6)] Hint: The Fourier transform of a Gaussian is another Gaussian. With r = 12, | d'r eh", ma'n? - 00) .- e-2/(41) Polar coordinate system with ê and în along the r- and z-axes, respectively, and k, =(kf sin coso, kf sino sino, kfcose).