484 Introduction to Quantum PhysicsP40.58Isolate the terms involving φin Equations 40.13 and 40.14. Square and add to eliminate .hmve20220222112λλθγ+′−′LNMOQP=cosSolve for vcbbc222=+ej:bhme=+′−′LNMOQP22002cos.Substitute into Eq. 40.12:11021222+FHGIKJ−′LNMOQP== −+FHGIKJ=+−hmcbcbce.Square each side:chcmhmchmeee20220222200211112+−′LNMOQP′LNMOQPFHGIKJ+′−′LNMOQPcos.From this we get Eq. 40.11:′−=FHGIKJ−01hecos.P40.59Show that if all of the energy of a photon is transmitted to an electron, momentum will not beconserved.Energy:hchcKmc021=′+=−bgif hc′=λ0(1)Momentum:hhmvγγ0=′if ′=∞(2)From (1),he01(3)vccee=−+FHGIKJ1002(4)Substitute (3) and (4) into (2) and show the inconsistency:cmc hchcheeeeeeee00002000020022FHGIKJ−+FHGIKJ=+++=+.This is impossible, so all of the energy of a photon cannot be transmitted to an electron.P40.60Begin with momentum expressions:
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This note was uploaded on 12/14/2011 for the course PHY 203 taught by Professor Staff during the Fall '11 term at Indiana State University .