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Schroedinger to another level

  1. Apr 22, 2006 #1
    ..i, am assured this is the right place for this thread -

    i, am interested in any arguments [ higher \ otherwise ] anyone may have, of: schroedinger's theory of QM ...in particula his differential QM wave equation, viz: solution Psi[x,t] giving the wave function to be associated with the motion of a particl of mass m under forces described by the potential energy function V[x,t], et cetera ..


  2. jcsd
  3. Apr 23, 2006 #2
    Um, I wonder if force can be a well-defined quantity in QM under potentials...

    I cannot say I agree with you about the "wave function associated with the motion of particle", rather I think Schrodinger equation smears the image of classical particle and no one really knows about what the wave function [tex]\Psi(x,t)[/tex] really is. Till this day, leading physicists admits that they don't exact understand the true nature of quantum mechanics in the documentary "The Elegant Universe".


    For me, [tex]|\Psi(x,t)|^2[/tex] and [tex]<\phi|\Psi(x,t)|\phi>[/tex] seems to have a more "physical meaning" than the wave function itself.

    It is important to notice that Schrodinger equation is a non-relativistic equation (Schrodinger tried unsuccessfully to formulate the quantum version). Schrodinger's equation can be deduced through conservation of energy assigning physical quantities to operators (with some ingenuity of course:rolleyes: ). We can write Schrodinger equation as simply as


    The next step towards a realtivistic "equation of motion" for quantum mechanics is the Klein-Gordon equation incoporating Einstein's energy-mass relation.

    http://en.wikipedia.org/wiki/Klein-Gordon_equation" [Broken]

    I'm not this advance yet on this issue, but I think that one major flaw of the Klein-Gordon equation is that it does not predict the "spin" of elctrons.
    The next step is the Dirac equation.

    http://en.wikipedia.org/wiki/Dirac_equation" [Broken]

    Dirac equation not only predicts spins, it also predicts the existence of antiparticle.
    Last edited by a moderator: May 2, 2017
  4. Apr 23, 2006 #3

    thank you Hyperreality. - have you an argument, for:


    ...giving the total probability of finding somewhere the particl described by the wave function [; the probability must equal one if there is a particl,] .... vis-a-vis: normalisation

    Last edited: Apr 23, 2006
  5. Apr 23, 2006 #4
    schroedinger's equation

    i, think :


    ..may; if, one assumes: schroedinger's equation to be right - is justifiable in QM history ..but: may be bettered, with: algebra and parallelising and apparelment; prehaps .. see the equation with the tautology, of; others !

    - substantsively, there is no doubt, of: schroedinger's greatness .

  6. Apr 23, 2006 #5
    the normalisation condition, namely

    [tex]\int^{-\infty}_{\infty} \psi^* \psi dx = 1[/tex]

    (at least for square integrable functions defined over [itex][-\infty, \infty][/tex]) is merely saying that the particle must exist somewhere.

    Also note that wavefunctions do not only describe particles; they are representations of the state vector in |x> basis.
    Last edited: Apr 23, 2006
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