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https://texercises.raemilab.ch/exercise/phase-and-group-velocity-for-electrons/
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Exercise:
Calculate the frequency wavelength and velocity for EkO electrons and verify that v_p lambda f c^/v_g.

Solution:
The frequency is f fracEh fF fracEe+Eknch fracEnch fracEJnch f resultfS The velocity is v vF sqrtfractimesEkm sqrtfractimesEkJm v resultvcP The wavelength is lambda frachp laF fracnchncme times v la resultlaP- The phase velocity is thus v_p vpF la times f vp resultvpcP The product of the group velocity v and the phase velocity v_p is v v_p vc times vpc prodc The deviation from the expected result c^ can be explained with the classical approximation for the electron's momentum.
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Exercise:
Calculate the frequency wavelength and velocity for EkO electrons and verify that v_p lambda f c^/v_g.

Solution:
The frequency is f fracEh fF fracEe+Eknch fracEnch fracEJnch f resultfS The velocity is v vF sqrtfractimesEkm sqrtfractimesEkJm v resultvcP The wavelength is lambda frachp laF fracnchncme times v la resultlaP- The phase velocity is thus v_p vpF la times f vp resultvpcP The product of the group velocity v and the phase velocity v_p is v v_p vc times vpc prodc The deviation from the expected result c^ can be explained with the classical approximation for the electron's momentum.
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Branches
quantum physics
Tags
de broglie, dispersion, electron, group velocity, phase velocity
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Difficulty
(2, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
Decoration