The stationary states of a two body system [Archive]

Phil Gardner

May3-04, 04:52 AM

Arnold Neumaier

May3-04, 05:48 PM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Phil Gardner wrote:\n> Any isolated two body system for which the total energy is constant\n> (no radiation in or out) would seem to be in a stationary state as is\n> the case for a hydrogen atom. All that quantum mechanics can predict\n> about any such state is contained in a wave function that satisfies a\n> time independent eigenvalue equation, a wave function that does not\n> travel, that does not evolve, that may collapse if and when the state\n> comes to an abrupt end. Isn\'t this true for any such two body system,\n> including all positive energy states of two interacting particles?\n\nAn isolated hydrogen atom at fixed total energy can still travel at\nconstant speed through space.\n\nMoreover, stationary does not mean the ground state,\nso any eigenstate of the reduced Hamiltonian gives rise to a stationary\nstate.\n\nBut in reality, it is not possible to isolate the hydrogen atom, since\nit is always coupled to ther electromagnetic field (part of which it\ngenerates), and thus all excited states will decay.\n\n\nArnold Neumaier\n\n\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Phil Gardner wrote:
> Any isolated two body system for which the total energy is constant
> (no radiation in or out) would seem to be in a stationary state as is
> the case for a hydrogen atom. All that quantum mechanics can predict
> about any such state is contained in a wave function that satisfies a
> time independent eigenvalue equation, a wave function that does not
> travel, that does not evolve, that may collapse if and when the state
> comes to an abrupt end. Isn't this true for any such two body system,
> including all positive energy states of two interacting particles?

An isolated hydrogen atom at fixed total energy can still travel at
constant speed through space.

Moreover, stationary does not mean the ground state,
so any eigenstate of the reduced Hamiltonian gives rise to a stationary
state.

But in reality, it is not possible to isolate the hydrogen atom, since
it is always coupled to ther electromagnetic field (part of which it
generates), and thus all excited states will decay.

Arnold Neumaier