5.73  Intro Quantum Mechanics I

Hi all,

Aaron asked what I meant by the effective field picture in problem 8d. The effective frequency weff is the hypotenuse of the right triangle formed by the off resonance frequency (w-wba) and the perturbing field strength in frequency units (Vab/hbar).  The effective field is proportional to wff by a constant,  the gyromagnetic ratio gamma.

One piece of background info that you should know (which I forgot to mention in class) is that magnetization precesses around the effective field axis at a frequency that is equal to weff. This is general. So depending on the angle of the effective field from the initial magnetization, you can trivially calculate where the magnetization vector lies on the precession trajectory after a certain time.  This is what problem 8d is about.

However, 8d was a bit mixed up. The original intention was to compare the on resonance and off resonance situations in (a) and (b). So I have modified problem 8's (c) and (d) together, to make it more interesting. The t=0 situation is trivial and not the intention. I will send the modified Pset 10 to you by email and upload it on line.

If you have other questions, I am available in my office on Sunday afternoon or Monday morning before 11. You can always ask by email.

Cheers,
Mei

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