By Epstein P.S., Ehrenfest P.
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Extra resources for The Quantum Theory of the Fraunhofer Diffraction
Example text
The most general solution to the full Schrödinger equation ih∂Ψ/∂t = HΨ is then given by applying exp(-iHt/h) to the wavefunction at some initial time (t=0) Ψ=Σ k Ckψk to obtain Ψ(t)=Σ k Ckψk exp(-itEk/h). The relative amplitudes Ck are determined by knowledge of the state at the initial time; this depends on how the system has been prepared in an earlier experiment. , the coordinates and momenta must be known at some initial time), the Schrödinger equation must be accompanied by initial conditions to fully determine Ψ(qj,t).
When L2 is measured the value L(L+1) h2 will be observed with probability |Dm,L |2, and the wavefunction for that particular sub-population will become ψ'' = ψL,m . At this stage, we know the value of L and of m, but we do not know the energy of the state. For example, we may know that the present sub-population has L=1, m=-1, but we have no knowledge (yet) of how much 2p-1, 3p -1, ... np -1 the system contains. To further probe the sample, the above sub-population with L=1 and m=-1 can be subjected to measurement of the energy.
2. An experimental measurement of any quantity (whose corresponding operator is F) must result in one of the eigenvalues fj of the operator F. These eigenvalues are obtained by solving Fφj =fj φj, where the φj are the eigenfunctions of F. Once the measurement of F is made, for that subpopulation of the experimental sample found to have the particular eigenvalue fj, the wavefunction becomes φj. , by spectroscopic means). The reader is strongly urged to also study Appendix C to gain a more detailed and illustrated treatment of this and subsequent rules of quantum mechanics.
The Quantum Theory of the Fraunhofer Diffraction by Epstein P.S., Ehrenfest P.
by George
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