Atomic Level Transitions

Yi-Zen Chu; Yiren Qu

<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>\n\nHello everyone,\n\nI just started learning QFT. I\'m wondering if QED tells us something\nabout the mechanism behind transitions within various atomic energy levels?\n\nFor instance, when an electron falls from an excited state to its ground\nstate can we use QFT to describe what exactly is going on? How much time\ndoes such a process to occur? Or does it make sense at all to ask such a\nquestion? How do we describe the emission of a photon? Why exactly do\natomic excited states decay - what\'s "wrong" with having a bit of excess\nenergy? Is there some sort of Lagrangian we can write down for this?\n\nThanks!\n\nYi-Zen\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>Hello everyone,

I just started learning QFT. I'm wondering if QED tells us something
about the mechanism behind transitions within various atomic energy levels?

For instance, when an electron falls from an excited state to its ground
state can we use QFT to describe what exactly is going on? How much time
does such a process to occur? Or does it make sense at all to ask such a
question? How do we describe the emission of a photon? Why exactly do
atomic excited states decay - what's "wrong" with having a bit of excess
energy? Is there some sort of Lagrangian we can write down for this?

Thanks!

Yi-Zen

Blake Winter

<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>\n\n\n"Yi-Zen Chu; Yiren Qu" <y_i_-_z_e_n_._c_h_u_@_y_a_l_e_._e_d_u> wrote in message news:<cll2uo\\$1bc\\$1@news.wss.yale.edu>...\n> Hello everyone,\n>\n> I just started learning QFT. I\'m wondering if QED tells us something\n> about the mechanism behind transitions within various atomic energy levels?\n>\n> For instance, when an electron falls from an excited state to its ground\n> state can we use QFT to describe what exactly is going on? How much time\n> does such a process to occur? Or does it make sense at all to ask such a\n> question? How do we describe the emission of a photon? Why exactly do\n> atomic excited states decay - what\'s "wrong" with having a bit of excess\n> energy? Is there some sort of Lagrangian we can write down for this?\n>\n> Thanks!\n>\n> Yi-Zen\nIt doesn\'t make any sense to ask the question you\'re asking - in QFT,\nas in classical mechanics, the atom will enter a superposition of\n"photon emitted" states and "photon not emitted" states. Likewise the\nphoton field (to use the term loosely) will enter a superposition of\nparticle number states. Of course the two will be entangled, but you\ncan\'t say for sure "when" a photon is emitted.\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>"Yi-Zen Chu; Yiren Qu[itex]" <y_{i_}-_z_e_n_._c_h_u_@_y_a_l_e_._e_d_u>[/itex] wrote in message news:<cll2uo$1bc$1@news.wss.yale.edu>...
> Hello everyone,
>
> I just started learning QFT. I'm wondering if QED tells us something
> about the mechanism behind transitions within various atomic energy levels?
>
> For instance, when an electron falls from an excited state to its ground
> state can we use QFT to describe what exactly is going on? How much time
> does such a process to occur? Or does it make sense at all to ask such a
> question? How do we describe the emission of a photon? Why exactly do
> atomic excited states decay - what's "wrong" with having a bit of excess
> energy? Is there some sort of Lagrangian we can write down for this?
>
> Thanks!
>
> Yi-Zen
It doesn't make any sense to ask the question you're asking - in QFT,
as in classical mechanics, the atom will enter a superposition of
"photon emitted" states and "photon not emitted" states. Likewise the
photon field (to use the term loosely) will enter a superposition of
particle number states. Of course the two will be entangled, but you
can't say for sure "when" a photon is emitted.

Arnold Neumaier

<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>Yi-Zen Chu; Yiren Qu wrote:\n\n> I just started learning QFT. I\'m wondering if QED tells us something\n> about the mechanism behind transitions within various atomic energy levels?\n>\n> For instance, when an electron falls from an excited state to its ground\n> state can we use QFT to describe what exactly is going on? How much time\n> does such a process to occur? Or does it make sense at all to ask such a\n> question? How do we describe the emission of a photon? Why exactly do\n> atomic excited states decay - what\'s "wrong" with having a bit of excess\n> energy? Is there some sort of Lagrangian we can write down for this?\n\nTransition between bound states are best studied with the approximation\nof QED called the Dirac-Fock equation.\n\nIn QED proper, even stating precisely what is an excited state is\ndifficult...\n\n\nArnold Neumaier\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>Yi-Zen Chu; Yiren Qu wrote:

> I just started learning QFT. I'm wondering if QED tells us something
> about the mechanism behind transitions within various atomic energy levels?
>
> For instance, when an electron falls from an excited state to its ground
> state can we use QFT to describe what exactly is going on? How much time
> does such a process to occur? Or does it make sense at all to ask such a
> question? How do we describe the emission of a photon? Why exactly do
> atomic excited states decay - what's "wrong" with having a bit of excess
> energy? Is there some sort of Lagrangian we can write down for this?

Transition between bound states are best studied with the approximation
of QED called the Dirac-Fock equation.

In QED proper, even stating precisely what is an excited state is
difficult...

Arnold Neumaier

Igor Khavkine

<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>On Wed, 27 Oct 2004 15:56:01 +0000, Yi-Zen Chu; Yiren Qu wrote:\n\n> Hello everyone,\n>\n> I just started learning QFT. I\'m wondering if QED tells us something about\n> the mechanism behind transitions within various atomic energy levels?\n\nThe conventional wisdom is that bound states in QFT are a mess, so no-one\napproaches them from that direction. And, at least in low energy atomic\nphysics, you don\'t need to.\n\n> For instance, when an electron falls from an excited state to its ground\n> state can we use QFT to describe what exactly is going on? How much time\n> does such a process to occur? Or does it make sense at all to ask such a\n> question? How do we describe the emission of a photon? Why exactly do\n> atomic excited states decay - what\'s "wrong" with having a bit of excess\n> energy? Is there some sort of Lagrangian we can write down for this?\n\nThe model for an electron making transitions between atomic levels is\nusually that of the electron sitting in an external potential interacting\nwith a quantized E&M field. The Hilbert space is the tensor product of\nelectronic bound states and the photon Fock space. Once interaction with\nthe E&M field is turned on you would expect the atomic energy levels to\nshift and the new eigenstates to become mixtures of states with different\nphoton numbers.\n\nIf you start your electron in one of the excited atomic states, it will\nnot be in an eigenstate that takes the E&M field into account, so it will\nhave overlap with one of these true eigenstates. But this true eigenstate\nwill also have overlap with the state where the electron fell a few levels\ndown and a photon carried the excess energy away. Hence there will be a\nnon-zero probability at some time in the future for the electron to fall\nfrom the excited atomic state and radiate a photon. The other direction is\npossible, if a photon comes in, there will be a probability that the\nelectron will absorb it and jump to an excited state. You might ask why\ndoesn\'t the electron get excited again after radiating some energy away.\nThe answer is simply that in this time dependent problem, radiation is\nemitted by an electron and escapes to infinity and doesn\'t come back.\n\nAtomic physicists do time dependent simulations of electronic transitions\nall the time. The duration of these events are known, and the slower ones\ncan even be observed using laser pulses with duration on the order of\nfemtoseconds.\n\nAn elementary treatment of an atom interacting with an E&M field can be\nfound in Advanced Quantum Mechanics by Sakurai. I\'m sure more detailed\ntreatments can be found in specialized texts on atomic physics.\n\nHope this helps.\n\nIgor\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>On Wed, 27 Oct 2004 15:56:01 [itex]+0000,[/itex] Yi-Zen Chu; Yiren Qu wrote:

> Hello everyone,
>
> I just started learning QFT. I'm wondering if QED tells us something about
> the mechanism behind transitions within various atomic energy levels?

The conventional wisdom is that bound states in QFT are a mess, so no-one
approaches them from that direction. And, at least in low energy atomic
physics, you don't need to.

> For instance, when an electron falls from an excited state to its ground
> state can we use QFT to describe what exactly is going on? How much time
> does such a process to occur? Or does it make sense at all to ask such a
> question? How do we describe the emission of a photon? Why exactly do
> atomic excited states decay - what's "wrong" with having a bit of excess
> energy? Is there some sort of Lagrangian we can write down for this?

The model for an electron making transitions between atomic levels is
usually that of the electron sitting in an external potential interacting
with a quantized E&M field. The Hilbert space is the tensor product of
electronic bound states and the photon Fock space. Once interaction with
the E&M field is turned on you would expect the atomic energy levels to
shift and the new eigenstates to become mixtures of states with different
photon numbers.

If you start your electron in one of the excited atomic states, it will
not be in an eigenstate that takes the E&M field into account, so it will
have overlap with one of these true eigenstates. But this true eigenstate
will also have overlap with the state where the electron fell a few levels
down and a photon carried the excess energy away. Hence there will be a
non-zero probability at some time in the future for the electron to fall
from the excited atomic state and radiate a photon. The other direction is
possible, if a photon comes in, there will be a probability that the
electron will absorb it and jump to an excited state. You might ask why
doesn't the electron get excited again after radiating some energy away.
The answer is simply that in this time dependent problem, radiation is
emitted by an electron and escapes to infinity and doesn't come back.

Atomic physicists do time dependent simulations of electronic transitions
all the time. The duration of these events are known, and the slower ones
can even be observed using laser pulses with duration on the order of
femtoseconds.

An elementary treatment of an atom interacting with an E&M field can be
found in Advanced Quantum Mechanics by Sakurai. I'm sure more detailed
treatments can be found in specialized texts on atomic physics.

Hope this helps.

Igor

DW

<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>The decay of excited states is induced by the fluctuation of vacuum. In\nthe fluctuation, all kinds of photons appear, these photons will\ninteract with electrons in an atom and causes transition. Of caurse, we\ncan use QFT to describe this process. But in atomic physics, I guess, we\nonly have to use field to describe the optical field. Dirac equation is\nenough to describe electrons. This sometimes called semiclassical\napproximation (? I am not sure). If you also use electron field, that\'s\nQED.\n\nYi-Zen Chu; Yiren Qu wrote:\n> Hello everyone,\n>\n> I just started learning QFT. I\'m wondering if QED tells us something\n> about the mechanism behind transitions within various atomic energy levels?\n>\n> For instance, when an electron falls from an excited state to its ground\n> state can we use QFT to describe what exactly is going on? How much time\n> does such a process to occur? Or does it make sense at all to ask such a\n> question? How do we describe the emission of a photon? Why exactly do\n> atomic excited states decay - what\'s "wrong" with having a bit of excess\n> energy? Is there some sort of Lagrangian we can write down for this?\n>\n> Thanks!\n>\n> Yi-Zen\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>The decay of excited states is induced by the fluctuation of vacuum. In
the fluctuation, all kinds of photons appear, these photons will
interact with electrons in an atom and causes transition. Of caurse, we
can use QFT to describe this process. But in atomic physics, I guess, we
only have to use field to describe the optical field. Dirac equation is
enough to describe electrons. This sometimes called semiclassical
approximation (? I am not sure). If you also use electron field, that's
QED.

Yi-Zen Chu; Yiren Qu wrote:
> Hello everyone,
>
> I just started learning QFT. I'm wondering if QED tells us something
> about the mechanism behind transitions within various atomic energy levels?
>
> For instance, when an electron falls from an excited state to its ground
> state can we use QFT to describe what exactly is going on? How much time
> does such a process to occur? Or does it make sense at all to ask such a
> question? How do we describe the emission of a photon? Why exactly do
> atomic excited states decay - what's "wrong" with having a bit of excess
> energy? Is there some sort of Lagrangian we can write down for this?
>
> Thanks!
>
> Yi-Zen

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