Re: Hydrogen in Relativistic QM

On Mon, 14 Nov 2005, Chris H. Fleming wrote:

> Is Hydrogen stable in relativistic quantum mechanics when you do not
> approximate the field as static? I am extra confused because
> positronium is not stable. The spiral occurs there. What is special
> about Hydrogen that stops the spiral?

Positronium isn't unstable because the electron "spirals" into the
positron. It is unstable because the electron and positron are
antiparticles, and hence the pair can annihilate into two photons. An
electron and a proton aren't mutual antiparticle, and hence cannot do
that.

In relativistic QM, just as in classical QM, the hydrogen problem has a
discrete spectrum of bound states. There is simply no way for an electron
to go into a lower state than the ground state (because there is no such
state), and hence the ground state is stable.

You seem to think in terms of classical orbits ("spiral"), but these don't
really exist in QM (whether classical or relativistic). An electron can
transition from a state of higher energy into a state of lower energy by
emitting a photon that carries away the energy difference. This is
sometimes referred to as a "quantum jump", and is the reason for the
spectra of discrete lines that you get from e.g. neon lamps.

Best wishes,

Georg

--
***************************************************************************
Dr. Georg M. von Hippel
Postdoctoral Research Fellow, Subatomic Theory Group

Department of Physics Phone: +1 (306) 337-2359
University of Regina Fax: +1 (306) 585-5659
Regina, Saskatchewan E-Mail: gmv22@xxxxxxxxxx
S4S 0A2 vonhippg@xxxxxxxxxx
Canada Web: http://uregina.ca/~vonhippg/
***************************************************************************

.

Relevant Pages

  • /zpf = (mc^2/e^2)^2(1 + (2/alpha)^2) for electron stability
    ... transverse EM waves have positive pressure? ... polarizations do have positive energy density hence negative pressure ... This gives the famous factor of 2 in Einstein's "gravity lens" ... physically the real on-mass-shell BARE electron sans its ...
    (sci.math)
  • /zpf = (mc^2/e^2)^2(1 + (2/alpha)^2) for electron stability
    ... transverse EM waves have positive pressure? ... polarizations do have positive energy density hence negative pressure ... This gives the famous factor of 2 in Einstein's "gravity lens" ... physically the real on-mass-shell BARE electron sans its ...
    (sci.physics.particle)
  • /zpf = (mc^2/e^2)^2(1 + (2/alpha)^2) for electron stability
    ... transverse EM waves have positive pressure? ... polarizations do have positive energy density hence negative pressure ... This gives the famous factor of 2 in Einstein's "gravity lens" ... physically the real on-mass-shell BARE electron sans its ...
    (sci.physics)
  • /zpf = (mc^2/e^2)^2(1 + (2/alpha)^2) for electron stability
    ... transverse EM waves have positive pressure? ... polarizations do have positive energy density hence negative pressure ... This gives the famous factor of 2 in Einstein's "gravity lens" ... physically the real on-mass-shell BARE electron sans its ...
    (sci.physics.relativity)
  • Cosmological Constant and Flying Saucers?
    ... Why the electron does not explode under its self-charge and why it ... I have also explained what gravity, dark energy and dark matter are! ... the self-electrical force at the surface of the typical EVO assumed ... Next consider a single electron as a shell of charge e at the ...
    (sci.math)