Re: relativistic wave equation

[newboltw <NewboltW@MADISON.ACAD.WLU.EDU>]

> Date:          Fri, 28 Jan 2000 10:16:25 -0500
> From:          Peter Schoch <pschoch@NAC.NET>
> Subject:       Re: relativistic wave equation
> To:            PHYS-L@lists.nau.edu
> Reply-to:      "phys-l@lists.nau.edu: Forum for Physics Educators"
>                <PHYS-L@lists.nau.edu>

> I haven't done anything with my QM since I left grad. school, so I may
> be out in left field; but, isn't the Dirac equation the relativistic
> form of the Schroedinger Eq.?
>
> Peter Schoch
> SCCC
>
> John Denker wrote:
> > At 02:19 PM 1/28/00 +0000, Kirkpatrick, James wrote:
> > >  ... In the case of Schrodinger's equation this is why it isn't
> > > consistent with special relativity.
> > >
> > > Might it not still be consistent with special relativity if the phase
> > > velocity and not the derivative of displacement is greater than c?
> >
> >   ==== Before answering that, let's consider an analogy ====
> >
> > Given the relativistic expression
> >          E^2 - p^2 = m^2
> > it is child's play (well, college freshman's play) to expand it to lowest
> > order and recover the classical result
> >          KE =  p^2 / 2m
> > This is a nice illustration of the correspondence principle.
> >
> > OTOH, starting from the classical non-relativistic result, it is *not*
> > child's play to discover how to generalize it to the relativistic case.
> >
> > ------------
> >
> > So it is with quantum mechanics.  There exist of course correct equations
> > of motion for relativistic quantum mechanics, and in the low-velocity limit
> > they reduce to the Schrödinger equation.
> >
> > OTOH the Schrödinger equation is not relativistically correct, and you
> > could stare at it for a verrry long time before it told you the correct
> > relativistic generalization.

I think it is fair to say that the Dirac Equation is the dynamic
equation that forms the basis of one kind of relativistic quantum
mechanics.  It seems to apply to the particle dynamics of certain
fermions (particles with spin 1/2).  So it applies to electrons,
protons, neutrons, and neutrinos.  It would not be expected to apply
to photons or pions -- they are bosons.  There is another form of
relativistic quantum mechanics that is applied to bosons.  It is
called the Klein-Gordon Equation.   Both of these relativistic
equations are quite different from the Schroedinger Equation, and I
believe they may not be derived from it just by applying a few
relativistic assumptions.                            WBN
Barlow Newbolt
Department of Physics and Engineering
Washington and Lee University
Lexington, VA 24450

Young man if I could remember the names of all of
these particles I would have become a botanist
                        Enrico Fermi
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