- #1
JDoolin
Gold Member
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I'd like to ask some questions about deBroglie waves.
(1) are deBroglie waves a topic under classical physics, or does it belong under quantum mechanics, or relativity?
(2) The justification for deBroglie expecting matter waves is "well, photons have frequency and wavelength, so it only makes sense that particles with mass should have frequency and wavelength, too." I have trouble believing that someone would be awarded a PhD, let alone a Nobel Prize for such an insipid analogy. Does anyone have any more detail on his reasoning?
(3) The wikipedia article alternates between saying the frequency is proportional to the kinetic energy (in the text) and the total energy (in the equations.) I am not sure I trust either idea. But on reading the wikipedia discussion page, I believe deBroglie originally meant for the Total Energy to be used.
However, if the (at rest) frequency is proportional to the rest mass energy, and the (at rest) wavelength approaches infinity. This can't be visualized. On the other hand, if you presume that the particle cannot be at rest (cf. Heisenberg's uncertainty principle), the wavelength is perhaps constrained by the container in which the particle is located?
(4) I am particularly curious about whether a space-time diagram of such a wave could be produced. The stationary particle would consist of a straight line. But would the waves, oscillating up and down form some surfaces in space-time.
I have an exercise from MTW's "Gravitation" Exercise 2.1 which gives
The problem is, as given, this equation is a nonlocalized wave; extending throughout space with the same amplitude! An actual particle should have a finite extension in space. Does de Broglie's explanation have some implicit boundary conditions?
(5) The experimental verification of de Broglie's hypothesis (Bragg diffraction, Fresnel diffraction, etc.) all seem to verify that the wavelength is in line with that predicted by deBroglie, but I don't see how these experiments verify the frequency is as deBroglie predicted.
(1) are deBroglie waves a topic under classical physics, or does it belong under quantum mechanics, or relativity?
(2) The justification for deBroglie expecting matter waves is "well, photons have frequency and wavelength, so it only makes sense that particles with mass should have frequency and wavelength, too." I have trouble believing that someone would be awarded a PhD, let alone a Nobel Prize for such an insipid analogy. Does anyone have any more detail on his reasoning?
(3) The wikipedia article alternates between saying the frequency is proportional to the kinetic energy (in the text) and the total energy (in the equations.) I am not sure I trust either idea. But on reading the wikipedia discussion page, I believe deBroglie originally meant for the Total Energy to be used.
However, if the (at rest) frequency is proportional to the rest mass energy, and the (at rest) wavelength approaches infinity. This can't be visualized. On the other hand, if you presume that the particle cannot be at rest (cf. Heisenberg's uncertainty principle), the wavelength is perhaps constrained by the container in which the particle is located?
(4) I am particularly curious about whether a space-time diagram of such a wave could be produced. The stationary particle would consist of a straight line. But would the waves, oscillating up and down form some surfaces in space-time.
I have an exercise from MTW's "Gravitation" Exercise 2.1 which gives
[tex]\psi = e^{i \phi}=exp[\vec k \cdot\vec x-\omega t][/tex]
as the "quantum mechanical properties of a de Broglie wave"The problem is, as given, this equation is a nonlocalized wave; extending throughout space with the same amplitude! An actual particle should have a finite extension in space. Does de Broglie's explanation have some implicit boundary conditions?
(5) The experimental verification of de Broglie's hypothesis (Bragg diffraction, Fresnel diffraction, etc.) all seem to verify that the wavelength is in line with that predicted by deBroglie, but I don't see how these experiments verify the frequency is as deBroglie predicted.