View Full Version : complex conjugate of wavefunction
alistair
Sep24-04, 08:11 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>The general wavefunction for a free particle is:\n\nY (x,t) = A cos( kx - wt) + iA sin (kx - wt)\n\nand the complex conjugate is:\n\nY*(x,t) = A cos( kx - wt) - iA sin (kx - wt)\n\nThese are multiplied together to give,along with a proportionality\nconstant,\nthe probability of finding a particle at a particular place at a\nparticular time.It is not known why this should be so.Here is a\nsuggestion:\n\nIf the wavefunction already represents a probability before it is\nsquared,\nthen multiplying it by another wavefunction - the complex conjugate -\nsuggests that we are dealing with the probability of two events\noccurring simultaneously.This could be the probability of a mass being\nin a particular place at a particular time, and something that is\nequivalent to the mass being at that place at the same time.Writing\nnew wavefunctions Y1 and Y2:\n\nY1 = A cos (kx - wt), Y2 = iA sin (kx -wt)\n\nthen Y = Y1 + Y2\n\nand Y* = Y1 - Y2\n\nThis is the kind of relation between wavefunctions that one gets\nfor a hydrogen molecule, for example.\nDoes anyone agree that the product YY* could be\ntelling us about two different particles in the same place at the same\ntime?\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 general wavefunction for a free particle is:
Y (x,t) = A cos( kx - wt) + iA sin (kx - wt)
and the complex conjugate is:
Y*(x,t) = A cos( kx - wt) - iA sin (kx - wt)
These are multiplied together to give,along with a proportionality
constant,
the probability of finding a particle at a particular place at a
particular time.It is not known why this should be so.Here is a
suggestion:
If the wavefunction already represents a probability before it is
squared,
then multiplying it by another wavefunction - the complex conjugate -
suggests that we are dealing with the probability of two events
occurring simultaneously.This could be the probability of a mass being
in a particular place at a particular time, and something that is
equivalent to the mass being at that place at the same time.Writing
new wavefunctions Y1 and Y2:
Y1 = A cos (kx - wt), Y2 = iA sin (kx -wt)
then Y = Y1 + Y2
and Y* = Y1 - Y2
This is the kind of relation between wavefunctions that one gets
for a hydrogen molecule, for example.
Does anyone agree that the product YY* could be
telling us about two different particles in the same place at the same
time?
John T Lowry
Sep27-04, 03:32 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"alistair" <alistair@goforit64.fsnet.co.uk> wrote in message\nnews:861c1b21.0409220427.1985d3ca@posting .google.com...\n> The general wavefunction for a free particle is:\n>\n> Y (x,t) = A cos( kx - wt) + iA sin (kx - wt)\n>\n> and the complex conjugate is:\n>\n> Y*(x,t) = A cos( kx - wt) - iA sin (kx - wt)\n>\n> These are multiplied together to give,along with a proportionality\n> constant,\n> the probability of finding a particle at a particular place at a\n> particular time.It is not known why this should be so.Here is a\n> suggestion:\n>\n> If the wavefunction already represents a probability before it is\n> squared,\n> then multiplying it by another wavefunction - the complex conjugate -\n> suggests that we are dealing with the probability of two events\n> occurring simultaneously.This could be the probability of a mass being\n> in a particular place at a particular time, and something that is\n> equivalent to the mass being at that place at the same time.Writing\n> new wavefunctions Y1 and Y2:\n>\n> Y1 = A cos (kx - wt), Y2 = iA sin (kx -wt)\n>\n> then Y = Y1 + Y2\n>\n> and Y* = Y1 - Y2\n>\n> This is the kind of relation between wavefunctions that one gets\n> for a hydrogen molecule, for example.\n> Does anyone agree that the product YY* could be\n> telling us about two different particles in the same place at the same\n> time?\n>\n\nYour error is in thinking the "Wave function already represents a\nprobability." Nope, it\'s just an amplitude, not a probability. For one\nthing, it\'s complex, not necessarily real.\n\nJohn Lowry\nFlight Physics\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>"alistair" <alistair@goforit64.fsnet.co.uk> wrote in message
news:861c1b21.0409220427.1985d3ca@posting.google.c om...
> The general wavefunction for a free particle is:
>
> Y (x,t) = A cos( kx - wt) + iA sin (kx - wt)
>
> and the complex conjugate is:
>
> Y*(x,t) = A cos( kx - wt) - iA sin (kx - wt)
>
> These are multiplied together to give,along with a proportionality
> constant,
> the probability of finding a particle at a particular place at a
> particular time.It is not known why this should be so.Here is a
> suggestion:
>
> If the wavefunction already represents a probability before it is
> squared,
> then multiplying it by another wavefunction - the complex conjugate -
> suggests that we are dealing with the probability of two events
> occurring simultaneously.This could be the probability of a mass being
> in a particular place at a particular time, and something that is
> equivalent to the mass being at that place at the same time.Writing
> new wavefunctions Y1 and Y2:
>
> Y1 = A cos (kx - wt), Y2 = iA sin (kx -wt)
>
> then Y = Y1 + Y2
>
> and Y* = Y1 - Y2
>
> This is the kind of relation between wavefunctions that one gets
> for a hydrogen molecule, for example.
> Does anyone agree that the product YY* could be
> telling us about two different particles in the same place at the same
> time?
>
Your error is in thinking the "Wave function already represents a
probability." Nope, it's just an amplitude, not a probability. For one
thing, it's complex, not necessarily real.
John Lowry
Flight Physics
<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\nalistair@goforit64.fsnet.co.uk (alistair) wrote in message news:<861c1b21.0409220427.1985d3ca@posting.google. com>...\n> The general wavefunction for a free particle is:\n>\n> Y (x,t) = A cos( kx - wt) + iA sin (kx - wt)\n>\n> and the complex conjugate is:\n>\n> Y*(x,t) = A cos( kx - wt) - iA sin (kx - wt)\n>\n> These are multiplied together to give,along with a proportionality\n> constant,\n> the probability of finding a particle at a particular place at a\n> particular time.It is not known why this should be so.Here is a\n> suggestion:\n>\n> If the wavefunction already represents a probability before it is\n> squared,\n> then multiplying it by another wavefunction - the complex conjugate -\n> suggests that we are dealing with the probability of two events\n> occurring simultaneously.This could be the probability of a mass being\n> in a particular place at a particular time, and something that is\n> equivalent to the mass being at that place at the same time.Writing\n> new wavefunctions Y1 and Y2:\n>\n> Y1 = A cos (kx - wt), Y2 = iA sin (kx -wt)\n>\n> then Y = Y1 + Y2\n>\n> and Y* = Y1 - Y2\n>\n> This is the kind of relation between wavefunctions that one gets\n> for a hydrogen molecule, for example.\n> Does anyone agree that the product YY* could be\n> telling us about two different particles in the same place at the same\n> time?\n\n\nWhat is the meaning of an event occuring that has a probability of i?\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>alistair@goforit64.fsnet.co.uk (alistair) wrote in message news:<861c1b21.0409220427.1985d3ca@posting.google.com>...
> The general wavefunction for a free particle is:
>
> Y (x,t) = A cos( kx - wt) + iA sin (kx - wt)
>
> and the complex conjugate is:
>
> Y*(x,t) = A cos( kx - wt) - iA sin (kx - wt)
>
> These are multiplied together to give,along with a proportionality
> constant,
> the probability of finding a particle at a particular place at a
> particular time.It is not known why this should be so.Here is a
> suggestion:
>
> If the wavefunction already represents a probability before it is
> squared,
> then multiplying it by another wavefunction - the complex conjugate -
> suggests that we are dealing with the probability of two events
> occurring simultaneously.This could be the probability of a mass being
> in a particular place at a particular time, and something that is
> equivalent to the mass being at that place at the same time.Writing
> new wavefunctions Y1 and Y2:
>
> Y1 = A cos (kx - wt), Y2 = iA sin (kx -wt)
>
> then Y = Y1 + Y2
>
> and Y* = Y1 - Y2
>
> This is the kind of relation between wavefunctions that one gets
> for a hydrogen molecule, for example.
> Does anyone agree that the product YY* could be
> telling us about two different particles in the same place at the same
> time?
What is the meaning of an event occuring that has a probability of i?
alistair
Sep29-04, 08:28 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>In message Alistair wrote:\n> The general wavefunction for a free particle is:\n>\n> Y (x,t) = A cos( kx - wt) + iA sin (kx - wt)\n>\n> and the complex conjugate is:\n>\n> Y*(x,t) = A cos( kx - wt) - iA sin (kx - wt)\n>\n> These are multiplied together to give,along with a proportionality\n> constant,\n> the probability of finding a particle at a particular place at a\n> particular time.It is not known why this should be so.Here is a\n> suggestion:\n>\n> If the wavefunction already represents a probability before it is\n> squared,\n\nIn message Igor wrote:\n>"What is the meaning of an event occurring that has a probability i?"\n\nI think that provided we are talking about two identical particles at\nthe same place at the same time then an imaginary wavefunction squared\nalways gives\na real probability for them.The imaginary probability (whatever such a\nthing is)\nfor each wavefunction does not represent the real world because\npresumably the\ntwo identical particles can never be separated.\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>In message Alistair wrote:
> The general wavefunction for a free particle is:
>
> Y (x,t) = A cos( kx - wt) + iA sin (kx - wt)
>
> and the complex conjugate is:
>
> Y*(x,t) = A cos( kx - wt) - iA sin (kx - wt)
>
> These are multiplied together to give,along with a proportionality
> constant,
> the probability of finding a particle at a particular place at a
> particular time.It is not known why this should be so.Here is a
> suggestion:
>
> If the wavefunction already represents a probability before it is
> squared,
In message Igor wrote:
>"What is the meaning of an event occurring that has a probability i?"
I think that provided we are talking about two identical particles at
the same place at the same time then an imaginary wavefunction squared
always gives
a real probability for them.The imaginary probability (whatever such a
thing is)
for each wavefunction does not represent the real world because
presumably the
two identical particles can never be separated.
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