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Schrodinger Equations - wave propagation

  1. Apr 29, 2009 #1
    Hi,
    Can somebody point me in the correct direction of learning about Schrodinger Equations in relation to Wave propagation. I came across Schrodinger Equations in some texts but couldn't quite understand some background. Most of the time the author used it from nowhere.

    Really appreciate if you would point me to some online / book references.
    Even wikipedia gives only a set of equations. I would hope some derivation/formulation based on Maxwell equations.

    Thanks
     
  2. jcsd
  3. Apr 29, 2009 #2
    What background do you have? If you are comfortable with Fourier transforms the Dover book Quantum Theory by David Bohm does a nice job motivating this.

    Note that Schrodenger's equation is not derived from Maxwell's equations.
     
  4. Apr 29, 2009 #3

    jtbell

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    Staff: Mentor

  5. Apr 29, 2009 #4
    Thanks.
    Yes I'm OK with Fourier transforms.
    I'm looking to understand the Schrodinger relationship in the context of wave propagation.

    http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/schrcn.html
    speaks only in abstract terms.


    So far I'm happily going through understanding dispersion, dielectric loss etc. But in several references I came across the Shrodinger equation but don't know how it fits in with wave propagation.
     
  6. Apr 30, 2009 #5
    Take the wave equation and you see that the solution can be written as
    φ(x,t) = A(x) e^{- i t w} where omega is the angular frequency. De Broglie says that the energy is E = \hbar w . Now you see that the Schrodinger equation id the square root of the wave equation.

    i \hbar ∂ φ(x, t) / ∂ t = E φ(x, t)
     
  7. Apr 30, 2009 #6
    Einstein says that.
     
  8. Apr 30, 2009 #7
  9. Apr 30, 2009 #8
    Thanks naturale !
    That was very clear.
    Anyway why is the wave equation represented as a schrodinger equation? Is there any particular importance related to wave propagation.

    I would really like to read some text with explanation like u gave + plus some insights in to the importance of representing in schrodinger equation. Could u point me to some?

    Thanks
     
  10. Apr 30, 2009 #9
    In the relativistic limit the Schrodinger equation becomes the KG equation, which (in particular in the massless case) represents a wave with velocity c. If you want to see the relation of the SE with wave equation you must study quantum field theory.

    To have an idea look to http://en.wikipedia.org/wiki/Klein-Gordon_equation .

    I don't how much in details you want to go, but on the interpretation of QM in terms of classical periodic waves my filling is that it is starting a new era.
     
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