Modern 2:More on Eigenfunctions and Measurements
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''I think I can safely say that no one understands quantum mechanics. -- R.P. Feynman'' | ''I think I can safely say that no one understands quantum mechanics. -- R.P. Feynman'' | ||
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===More on the time/energy uncertainty relation=== | ===More on the time/energy uncertainty relation=== | ||
Revision as of 15:27, 1 March 2006
I think I can safely say that no one understands quantum mechanics. -- R.P. Feynman
Notice the Dirac bra-kets on the blackboard.
More on the time/energy uncertainty relation
In quantum mechanics time plays a fundamentally different role than other observables. Conisder the official definition
The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.
In other words, the frequency of the photons which are resonant with this transition in the ground state of Cs is exactly 9192631770 Hz = 9.192631770 GHz
ultra narrow spectra in a modern atomic clock
The key idea is: the longer the lifetime of an excited state, the narrower its spectral line. Mathematica notebook on time/frequency uncertainty for Gaussians
But what we really measure is not time at all, it's frequency.
Never measure anything but frequency: Arthur Schawlow
Shawlow was the co-inventor of the laser and got the Nobel Prize in 1981. Schawlow's very interesting Nobel lecture
