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Wave-Particle Duality

  1. Jun 28, 2006 #1
    There seems to be a need for a theory that explains both the particle and wave properties of the electron. Neils Bohr treated the proton and electron as point-charges and successfully calculated the energy levels. He attempted to explain the stability of the h-atom by suggesting the planetary model and circular orbits that do not radiate energy. However, he did not account for the wave properties of the electron. On the other hand, quantum mechanics uses the wave properties to explain hydrogen's spectral lines, yet fails to address the stability of the h-atom or its particle properties. Just my observation. Could some comment on a unified theory incorporating both properties.
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  3. Jun 28, 2006 #2


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    J.S. Bell once wrote about the two-slit experiment (where the "dual" nature of the electron is most manifest): "Is it not clear from the smallness of the scintillation on the screen that we have to do with a particle? And is it not clear, from the diffraction and interference patterns, that the motion of the particle is directed by a wave? DeBroglie showed in detail how the motion of a particle, passing through just one of two holes in the screen, could be influenced by waves propagating through both holes. And so influenced that the particle does not go where the waves cancel out, but is attracted to where they cooperate. This idea seems to me so natural and simple, to resolve the wave-particle dilemma in such a clear and ordinary way, that it is a great mystery to me that it was so completely ignored."

    You can find out more about this "natural and simple" (but unfortunately still largely ignored) theory here:

  4. Jun 28, 2006 #3
    QM does describe both wave-like and particle-like behavior of the same particle. Classical descriptions are ultimately insufficient; it will not work to describe an electron as a classical point particle, nor a classical wave. QM is very different.

    So? Schrodinger's wave mechanics can do that also. Keep in mind Bohr's model was the very first of its kind back then, it has many shortcomings - for example, it doesn't know how to deal with two electrons and so it can't get the spectrum of Helium.

    You've got it backwards - QM was the first to succeed in explaining the stability of atoms - it was the earlier, primitive models like Bohr atom which failed at this.
  5. Jun 28, 2006 #4
    Why would a new student hasn't even studied QM, be interested in foundational issues like the Bohm interpretation? :confused:
  6. Jun 28, 2006 #5


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    I thought I was the only one who noticed this. :rofl: For ttn, oQM is simply "wrong" while Bohmian Mechanics is "right". I wish I could see things in such black and while terms.
  7. Jun 28, 2006 #6
    What dilemma?
  8. Jun 29, 2006 #7
    Quantum mechanics does not explain the stability of the ground state electron of the h-atom where it is postulated that the angular momentum is zero. If there is no circular motion why doen't the electron fall into the nucleus of the atom? At least Bohr attempted to expalin the stability of the atom by proposing a dynamic equilibrium between the proton and electron, that is, the planetary model.
  9. Jun 29, 2006 #8
    Have you solved the energy eigenvalue problem for the Hydrogen atom?

    There are a number of energy eigenstates that come out; and the state of lowest energy is at -13.6eV. The rules of quantum mechanics don't allow there to be any lower state. Applying the angular momentum operator on that state gives an angular momentum of zero. That perfectly explains everything.

    Whoever said anything about circular motion? Does it even make sense to say such a thing? Motion requires position and momentum at every instant to specify it's path. Quantum mechanics prohibits a system being in state of definite position and momentum at the same time, so one's notions of classical motion do not apply to electrons in the H atom.

    Bohr's ideas were good for the time, but are a poor model compared to what we have now.
  10. Jun 29, 2006 #9
    Yes I have calcuated the eigenstated which are purely mathematical. Where is the connection to the h-atom? In physics you start with a model and then write the mathematics to explain the model. Quantum mechanic avoids explaining the stability of the h-atom based on basic principles of physics. To say circular motion does not make sense or classical physics does not apply is avoiding the physical basis for hydrogen's spectral lines. Are you saying the h-atom is not real and therefore no physical basis is needed?
  11. Jun 29, 2006 #10


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    Er... look at the energy eigeinvalues that you get. It doesn't match experimental observations?

    Er... it doesn't?

    So what other physics do you wish to invoke to explain the stability of H atom? Classical E&M?

    I would like to see you use classical physics to "explain" the bonding H-atom makes, or even to derive accurately H-spectra especially when you apply a magnetic field to it. Or what about we stick in the Stark effect? If you can show such derivation that fits the experimental observation, I'll help you write a paper to AJP.

    What is a "physical basis"? What can be more physical than when it agrees QUANTITATIVELY with experimental observation?

  12. Jun 29, 2006 #11
    When you say electrons have circular motion in the H atom, what you mean is, you have a model of the H atom where the electrons move in circular orbits. From that model, you can extract some consquences, like how much EM radiation will be emitted and the path of the electron as a function of time etc.

    When you compare that with reality via experiments, what you find is utter disagreement between the two.

    So you come up with another model. In this model, we have operators, and eigenstates, and Schrodinger's equation (among other things), and we call it QM. Using that model, we derive consequences, like there is a ground state, no radiation is emitted unless the electron jumps between energy levels etc. etc.

    We now compare this model with the reality, and find good agreement, but not perfect. We refine our model: add the relativistic K.E. correction, account for spin-orbit coupling etc. We get better agreement and so on.

    By doing this, we can say that QM provides a better model of reality, at the microscopic scale, than classical mechanics.

    What could be more basic than the principles of conservation of energy, momentum and angular momentum?
  13. Jun 29, 2006 #12
    Yes the energy eigeinvalues match the experimental values (and yes quantum mechanics agrees quantitatively with experimental observation) but so do the Bohr values. What physics would I use? I would obey the laws and principles of classical physics, Maxwell's equations, and conservation of angular momentum. Predicting the energy levels in itself does not equate to a physical basis. Any complete theory must not simply postulate nonradiating states but supply a physical basis for non-radiating states in an electric field.
  14. Jun 29, 2006 #13
    But nature doesn't obey classical physics and Maxwell's equations, isn't that enough? You've taken a QM course, it should have been obvious throughout.

    As for why the 94-year old Bohr model is inferior to actual QM, do we really need to go through this?
    -Doesn't explain anything other than spectra of hydrogen-like atoms; fails at helium, everything else
    -Cannot explain molecular bonding or any multiatomic physics
    -Cannot explain Stark or Zeeman shifts quantitively
    -Cannot explain interactions of light (photons) with matter (atoms)
    -It doesn't even fit into classical physics - it requires violation of Maxwell's equations by posulating that electrons do not radiate in atoms!
  15. Jun 29, 2006 #14
    You've got to realize that you're requiring physical law to a priori take a given physical form - classical mechanics and EM - and that is not science.
  16. Jun 29, 2006 #15
    Of course the Bohr model fails and as you stated it violates Maxwell's equations. So your conclusion is that the electron can't be explain by classical physics or that classical physics fails. It seems to me the only conclusion is that the Bohr model failed. I am not ready to accept the other. What is not science is a mathematical model incapable of any conceptual model of the h-atom.
  17. Jun 29, 2006 #16
    By 'conceptual', do you mean anything stronger than "it satisfies everyday physical intutition?" That kind of criterea is quite irrelevant to science.

    You need to get acquanited with the fundamental experiments themselves, which convinced half a century of physcists that classical physics just doesn't work. Famous experiments like
    -Stern-Gerlach, non-commuting measurements
    -Double-slit interference and all it's variations - including single-photon interference
    -Diffraction of massive particles (electrons)
    -Aspect's experiment, tests of bell's inequality violation (entangled particles)
  18. Jun 29, 2006 #17
    It was a lucky coincedence that classical physics happened to be a good model of reality for macroscopic systems and and for it to be easy to visualise. But QM never claimed to be both; QM claims to be a good model of reality on the microscopic scale, and that is what it is.

    If you object that QM is not easy conceptually, then fine. That's your opinion. But you cannot claim that QM is not a good model of reality on the microscopic scale; for that is what it is.

    So, what is your objection? And why, as you have claimed, is QM's model of the H atom not a "conceptual model"?
    Last edited: Jun 29, 2006
  19. Jun 29, 2006 #18


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    But it doesn't! The Bohr model failed when you put that same H atom in a magnetic field, or an electric field! Try it. It's in the DETAILS of the spectrum that shows that the the QM description works.

    Besides, what makes you think that you can simply judge the validity of something based on ONE data point? Have we not gone beyond the H-atom already today? Try the Rydberg formula on heavier atoms and see to what extent you get it right and to what extent the results become ridiculously wrong. You are using the ONE instant where the Bohr model somewhat got it right under a certain condition and using it to justify its validity while ignoring a whole zoo of observations where it doesn't even come close. I fail to see the rationality in this.

  20. Jun 30, 2006 #19
    **By 'conceptual', do you mean anything stronger than "it satisfies everyday physical intutition?" That kind of criterea is quite irrelevant to science.

    You need to get acquanited with the fundamental experiments themselves, which convinced half a century of physcists that classical physics just doesn't work. Famous experiments like***

    -Stern-Gerlach, non-commuting measurements

    Wrong: see Barut and Zanghi (1984), Ranada and Ranada (1979), Barut (1986)

    -Double-slit interference and all it's variations - including single-photon interference

    Wrong: a non-linear classical field theory can account for that (Barut 1984 and next years where soliton like solutions to the self coupled Dirac Maxwell equations were developed).

    -Aspect's experiment, tests of bell's inequality violation (entangled particles)

    These things could be very well based upon a misunderstanding of QM (and there has never been any violation of the Bell inequalities for the bare data WHEN the former were applicable in the first place !).

    Your convincing evidence is already long time refuted.

  21. Jun 30, 2006 #20
    I agree quantum mechanics has provided additional insight to the wave properties of the electron with many applications in other areas. What is important is the wave property. This aspect of the theory is certainly correct. Does that mean the entire theory is correct?

    However, what happen to the particle property. If asked to calculate the force on the electron bound to the proton you would you the classical force equation and treat the particles as point-charges. But, when asked to calculate the energy states treating the particles as point-charges with wave motion you say classical physics does not apply. Quantum mechanics claims to completely solve the h-atom based on its wave properties and yet the wave equation, psi, has no physical meaning, and quantum mechanics cannot explain the wave motion of the electron bound to the h-atom. Psi is a complex function and cannot be used to describe a real wave in any kind of orbit (circular or otherwise). I do not claim the Bohr atom is correct, but has some value. There must be a middle ground between the Bohr model and quantum mechanics in which a real wave equation is used to completely solve the h-atom mystery.
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