Hari Seldon
Jun11-04, 06:29 AM
<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\nHi,\n\nOk, I asked this before, in a somewhat different way and since I did\nnot get any satisfying answer I\'ll try again, with a simpler example.\nSuppose we have a source (S), emitting a photon at time t and a\ndetector (D) detecting the photon at time t\', where t\' > t. Now my\nquestion is very simple and perhaps the answer is also very simple.\nHow do you calculate the amplitude to detect the photon emitted by S\nat t at the detector D at time t\'. I can think of two ways to do so.\n\n1) Use the path integral method of quantum mechanics. This means we\nmust assume the photon is initially at time t, in some state |i,t> and\nupon detection in some state |f,t\'>. The question is, what does the\ninitial (or final) state look like. First of all, can a photon be in a\nposition eigenstate? (I ask this because I heard there were problems\nwith defining a position representation wave function). I guess the\nbest description for the initial state is some superposition of\nmomentum (and position?) states, since the particle is fairly\nlocalised and we know the momentum is only in the direction of D. So\nwhat would it look like? Then if I know this, the final state looks\nsimilar. Then are there any problems with summing over all paths\nbetween these states? Or does it work exactly as with the electon. I\nask this because I still wonder whether we can apply this quantum\nmechanical principle to the photon since the photon is necesarilly a\nrelativistic particle. Don\'t we need at least relativistic quantum\nmechanics? What changes then? Or do we actually need field theory ?\nThis brings me to option 2.\n\n2) We assume the photon is in fact a virtual photon, part of a QED\ndiagram. This amplitude for the described \'experiment\' is then given\nby the photon propagator (dressed propagator?). Or is it perhaps given\nby the whole amplitude of all the corresponding diagrams for the\nprocess of emitting a photon and absorbing a photon as given by for\nexample: >---<.\n\nAs you can see I am quite confused about this simple example. I hope\nsomeone can help me nevertheless.\n\nMany thnx,\n\nHari.\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>Hi,
Ok, I asked this before, in a somewhat different way and since I did
not get any satisfying answer I'll try again, with a simpler example.
Suppose we have a source (S), emitting a photon at time t and a
detector (D) detecting the photon at time t', where t' > t. Now my
question is very simple and perhaps the answer is also very simple.
How do you calculate the amplitude to detect the photon emitted by S
at t at the detector D at time t'. I can think of two ways to do so.
1) Use the path integral method of quantum mechanics. This means we
must assume the photon is initially at time t, in some state |i,t> and
upon detection in some state |f,t'>. The question is, what does the
initial (or final) state look like. First of all, can a photon be in a
position eigenstate? (I ask this because I heard there were problems
with defining a position representation wave function). I guess the
best description for the initial state is some superposition of
momentum (and position?) states, since the particle is fairly
localised and we know the momentum is only in the direction of D. So
what would it look like? Then if I know this, the final state looks
similar. Then are there any problems with summing over all paths
between these states? Or does it work exactly as with the electon. I
ask this because I still wonder whether we can apply this quantum
mechanical principle to the photon since the photon is necesarilly a
relativistic particle. Don't we need at least relativistic quantum
mechanics? What changes then? Or do we actually need field theory ?
This brings me to option 2.
2) We assume the photon is in fact a virtual photon, part of a QED
diagram. This amplitude for the described 'experiment' is then given
by the photon propagator (dressed propagator?). Or is it perhaps given
by the whole amplitude of all the corresponding diagrams for the
process of emitting a photon and absorbing a photon as given by for
example: >---<.
As you can see I am quite confused about this simple example. I hope
someone can help me nevertheless.
Many thnx,
Hari.
Ok, I asked this before, in a somewhat different way and since I did
not get any satisfying answer I'll try again, with a simpler example.
Suppose we have a source (S), emitting a photon at time t and a
detector (D) detecting the photon at time t', where t' > t. Now my
question is very simple and perhaps the answer is also very simple.
How do you calculate the amplitude to detect the photon emitted by S
at t at the detector D at time t'. I can think of two ways to do so.
1) Use the path integral method of quantum mechanics. This means we
must assume the photon is initially at time t, in some state |i,t> and
upon detection in some state |f,t'>. The question is, what does the
initial (or final) state look like. First of all, can a photon be in a
position eigenstate? (I ask this because I heard there were problems
with defining a position representation wave function). I guess the
best description for the initial state is some superposition of
momentum (and position?) states, since the particle is fairly
localised and we know the momentum is only in the direction of D. So
what would it look like? Then if I know this, the final state looks
similar. Then are there any problems with summing over all paths
between these states? Or does it work exactly as with the electon. I
ask this because I still wonder whether we can apply this quantum
mechanical principle to the photon since the photon is necesarilly a
relativistic particle. Don't we need at least relativistic quantum
mechanics? What changes then? Or do we actually need field theory ?
This brings me to option 2.
2) We assume the photon is in fact a virtual photon, part of a QED
diagram. This amplitude for the described 'experiment' is then given
by the photon propagator (dressed propagator?). Or is it perhaps given
by the whole amplitude of all the corresponding diagrams for the
process of emitting a photon and absorbing a photon as given by for
example: >---<.
As you can see I am quite confused about this simple example. I hope
someone can help me nevertheless.
Many thnx,
Hari.