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A Why is the Matter wave analogous to photon and derived from it?

  1. Feb 8, 2017 #1
    The electromagnetic wave derivation uses the fact that charge enclosed is zero and it goes to obey plane wave equations.

    Lets say we were deriving a wave equation from maxwell's equations for electron wave motion, but we assume that charge enclosed is not zero, and come up with some differential equation not like the standard wave equation. Using this if we were to find the wavelength, and lets say that wavelength is 95% of the de-broglie wavelength, then would it not be more better to use this new wave equation, rather than photon equation which assumes charge is zero.

    ph207-h7-gauss-e-m.GIF

    One can say that matter wave has nothing to do with charge, but whenever its derivation is done, its assumed as plane wave, which is obeyed by charge less particle like photon. If there is another, lets say Quack-wave, which is derived taking charge enclosed as e and J≠o, what would be the basis for rejecting quack- wave over plane wave.

    Note: Assume that the wavelength using quack-wave is independent of the charge itself, therefore will work for neutral atoms also, just assume that quack wave equation gives a different constant C which gives us the matter wave as C * de-broglie wavelength.
     
    Last edited: Feb 8, 2017
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  3. Feb 8, 2017 #2

    PeterDonis

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    Have you tried this? What equation did you come up with?
     
  4. Feb 9, 2017 #3
    What i have tried, is found out the condition for electron to physically undulate in external applied time-varying magnetic field of frequency f. The electron moves with the condition that no matter how much its velocity decreases/increases, its frequency(f) remains the same throughout.

    I did its simulation and found out that the electron did move in undulatory pattern with fixed frequency, even when i changed the initial velocity. The simulation has not however taken the induced electric field into account, but electric force in any case acts tangent to the particle trajectory and imparts it kinetic energy, thereby increasing its velocity in half time period, and decreasing it in 2nd half. Since the electron will complete its cycle in fixed time(1/f) no matter what its velocity is, the induced electric field doesn't change the frequency of electron.

    Importantly: In order to compare with de-broglie wavelength what i did is try to make electron move with frequency determined by E/h. Then insert the frequency in my equation and find the wavelength, then compare it with h/p. I found that everytime my wavelength was smaller by approx 5.3% which is constant.

    Why is the physical undulating wavelength(in external magnetic field) even close to the matter wave wavelength ?
     
  5. Feb 9, 2017 #4

    PeterDonis

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    Using what equations?

    This doesn't make sense. Particles with nonzero rest mass still have a dispersion relation (variation of energy/frequency with speed/momentum). It's just not exactly the same as the one for massless particles.

    I'm not sure why you would need to; can't the equations be solved analytically?
     
  6. Feb 9, 2017 #5
    Consider the electron motion in cyclotron, there the external voltage increases the kinetic energy of the electrons, yet they complete the cycle with fixed frequency. The equation i derived is from the basic cyclotron equation itself !

    I performed the simulation to verify if the equations are causing the electrons to go in that fashion using already developed model library of cyclotron.
     
  7. Feb 9, 2017 #6

    PeterDonis

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    That's because the external magnetic field strength is increased as the electron energy increases. If that were not done, the electrons would not stay inside the cyclotron. Are you taking that into account?

    Also, the frequency of the electron's motion around the cyclotron has nothing to do with the frequency of the electron's matter wave.
     
  8. Feb 9, 2017 #7
    NO! NOT AT ALL.......the cyclotron frequency is independent of the velocity itself :
    http://www.electrical4u.com/cyclotron-basic-construction-and-working-principle/
     
  9. Feb 9, 2017 #8

    PeterDonis

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    What does this have to do with anything? I think you are confused. Your OP was talking about the frequency of the electron's matter wave; now you are talking about the frequency of the electron's orbits in a cyclotron. Those are not the same thing. The fact that the latter frequency is independent of the electron's velocity is irrelevant to that point.
     
  10. Feb 9, 2017 #9
    What i meant to say was that the magnetic field strength need not change in cyclotron motion. So in my OP i can choose the frequency, and then determine the peak magnetic field strength accordingly to allow me to undulate the electron in that frequency. So determining the frequency from E/h and then finding the wavelength gave an almost close wavelength to matter wave and the electron undulating wavelength.
     
  11. Feb 9, 2017 #10

    PeterDonis

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    If the cyclotron is set up as a spiral instead of a circle, yes, this is true; the electron just spirals outward.

    You can choose the frequency at which the electron goes around the cyclotron, yes. But, once more, that has nothing to do with the frequency of the electron's matter wave. You continue to ignore this point even though I have made it repeatedly.

    Is wrong. See above.
     
  12. Feb 9, 2017 #11
    Well i see this has led to some confusion from my side, pls let me clarify:
    raytondENG.png

    Consider the electron moving as shown, but in the fig. you can see that the wavelength of electron trajectory remains constant. My case has very similar trajectory, but the frequency is constant , and if radiation doesn't occur then the wavelength will not change either. The matter wave has complex components and is not the same as physical undulation of particle......yet when i physically do undulate the particle, it gives very close wavelength to matter wave, where the VALUE of the frequency i take for that undulation is calculated by E/h, where E is K.E. of the electron.
     
  13. Feb 9, 2017 #12

    PeterDonis

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    What wavelength are you talking about? Please show some math.

    Again, please show some math. This is looking more and more like your own personal theory, and personal theories are off limits at PF. If you cannot show some standard math describing what you are doing this thread will be closed.
     
  14. Feb 9, 2017 #13
    I haven't done any publication work on this yet but here are the theory and math:
     

    Attached Files:

  15. Feb 9, 2017 #14

    PeterDonis

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    In other words, at this point it's your personal theory. If you ever get it published in a peer-reviewed journal, then it might be suitable for discussion here. Until then, it's off limits. Thread closed.
     
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