Subject: CCL:time-dependent and time-independent QM

From: <victor_anisimov-.at.-comcast.net>
Date: Tue, 13 Jul 2004 00:25:47 -0400

----- Original Message ----- 
From: <hinsen-.at.-cnrs-orleans.fr>
To: "Shobe, David" <dshobe-.at.-sud-chemieinc.com>
Cc: "CCL computational chemistry list (E-mail)" <chemistry-.at.-ccl.net>
Sent: Monday, July 12, 2004 4:52 PM
Subject: CCL:time-dependent and time-independent QM

> On 12.07.2004, at 22:14, Shobe, David wrote:
> 
> > Where does the part where measuring a property of the system "resets"  
> > the quantum state of the system come in?   That's always been  
> > mysterious:
> 
> That depends on who you ask, I think that discussion is still  
> open-ended. The "collapse of the wave function" is part of the original  
> Copenhagen interpretation of the meaning of the wave function. However,  
> there are other interpretations. As the term "interpretation" implies,  
> the choice of one does not change the maths - the equations and wave  
> functions remain the same.
> 
> The real problem in that discussion is that "measurement" needs to be  
> defined. In a pure quantum world, there are particles interacting, all  
> subject to the same laws, and the whole universe is governed by a  
> single huge wave function. No measurements, no problems. Various  
> definitions of measurements have been proposed, but none has yet been  
> found to be without problems. Some say that measuring implies human  
> consciousness - hence the paradox known as "Schrvdinger's cat". Others  
> say that measurement is an interaction with a classical object, but  
> that would imply that quantum mechanics needs to be defined in terms of  
> its own limiting case, classical mechanics.

Perhaps the term "measurement" is already satisfactorily defined in quantum 
mechanics. The "measurement" of a physical property, which is an operator |p|,
e.g. impulse, is a mean value <W|p|W> where W is wavefunction of the
system. Thus we know how to perform "measurement". The quantum problem, 
which is associated with the process  of "measurement" is related to the fact that 
those operators, which do not commute, like energy |E| and impulse |p| yield different 
results depending of their order. Thus, |E*p| operator is different from its |p*E| 
counterpart and being applied to wavefunction they would yield different results. This 
leads to the well-known statement that one can not measure energy and impulse at 
the same time. Commuting operators, like energy and dipole moment do not show 
such restriction.

Supposedly this has little to do with "interpretation" but this is rather a mathematical 
apparatus of quantum mechanics that can be either confirmed or rejected by
experiment. So far we know only confirmations.

With kind regards,
Victor

--
Victor Anisimov
School of Pharmacy
University of Maryland

---

From: "Xavier ASSFELD" <Xavier.Assfeld|at|lctn.uhp-nancy.fr>
Date: Tue, 13 Jul 2004 14:36:42 +0200

X> -----Message d'origine-----
X> De : Computational Chemistry List [mailto:chemistry-request|at|ccl.net]De
X> la part de victor_anisimov|at|comcast.net
X> Envoyi : mar. 13 juillet 2004 06:26
X> @ : hinsen|at|cnrs-orleans.fr; Shobe, David
X> Cc : CCL computational chemistry list (E-mail)
X> Objet : CCL:time-dependent and time-independent QM
X>
X> Perhaps the term "measurement" is already satisfactorily defined
X> in quantum
X> mechanics. The "measurement" of a physical property, which is an
X> operator |p|,
X> e.g. impulse, is a mean value <W|p|W> where W is wavefunction of the
X> system. Thus we know how to perform "measurement". The quantum problem,
X> which is associated with the process  of "measurement" is
X> related to the fact that
X> those operators, which do not commute, like energy |E| and
X> impulse |p| yield different
X> results depending of their order. Thus, |E*p| operator is
X> different from its |p*E|
X> counterpart and being applied to wavefunction they would yield
X> different results. This
X> leads to the well-known statement that one can not measure
X> energy and impulse at
X> the same time. Commuting operators, like energy and dipole
X> moment do not show
X> such restriction.
X>

Just my 2 eurocents,
I think that the problem of measuring something of a quantum system is
related to the superposition state. A quantum system can be in a
superposition of eigenstate, e.g. a hydrigen atom can be in state Y = c1*1s
+c2*2s. When you measure in which state the hydrogen atom is, you will find
c1*c1 times the energy of the 1s state and c2*c2 times the energy of the 2s
state. You'll never find c1*c1*E1+c2*c2*E2 value! When you measure the
energy the wavefunction is "reduced" to only one eigenstate.
Hope that I throw oil on fire...
Yours

X> Supposedly this has little to do with "interpretation" but this
X> is rather a mathematical
X> apparatus of quantum mechanics that can be either confirmed or
X> rejected by
X> experiment. So far we know only confirmations.
X>
X> With kind regards,
X> Victor
X>
X> --
X> Victor Anisimov
X> School of Pharmacy
X> University of Maryland
X>
X>
X>
X> -= This is automatically added to each message by the mailing script =-
X> To send e-mail to subscribers of CCL put the string CCL: on your
X> Subject: line
X> and send your message to:  CHEMISTRY|at|ccl.net
X>
X> Send your subscription/unsubscription requests to:
X> CHEMISTRY-REQUEST|at|ccl.net
X> HOME Page: http://www.ccl.net   | Jobs Page: http://www.ccl.net/jobs
X>
X> If your mail is bouncing from CCL.NET domain send it to the maintainer:
X> Jan Labanowski,  jlabanow|at|nd.edu (read about it on CCL Home Page)
X> -+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
X>
X>
X>
X>
X>

                                      ...Xav

Pr. Xavier Assfeld                  Xavier.Assfeld|at|lctn.uhp-nancy.fr
Laboratoire de Chimie thiorique     (T) 33 3 83 68 43 82
Universiti Henri Poincari           (F) 33 3 83 68 43 71
F-54506 Nancy B.P. 239              http://www.lctn.uhp-nancy.fr

---

From: hinsen|at|cnrs-orleans.fr
Date: Tue, 13 Jul 2004 09:19:53 +0200

On 13.07.2004, at 06:25, <victor_anisimov|at|comcast.net> wrote:

> system. Thus we know how to perform "measurement". The quantum

Then what is the physical procedure to obtain the mean value?  
Measurement is a physical operation, not a mathematical one.

> apparatus of quantum mechanics that can be either confirmed or  
> rejected by experiment. So far we know only confirmations.

It is true that quantum mechanics is largely confirmed by experiment,  
but that doesn't resolve the question of the definition of measurement.  
The different interpretations that have been proposed for the wave  
function make no difference for the experiments that have been devised  
so far, otherwise the issue might have been settled by now.

I suspect that ultimately the problem is an artificial one, that  
"measurement" is an unnecessary idealization that doesn't fit the  
quantum world. Any experimental setup can be described by quantum  
mechanics, even though the maths may be too complicated to do the  
computations explicitly. An apparatus suitable for "measurement" is  
simply one whose states are sufficiently distinct to permit observation  
by human sensory organs.

------------------------------------------------------------------------ 
-------
Konrad Hinsen
Laboratoire Leon Brillouin, CEA Saclay,
91191 Gif-sur-Yvette Cedex, France
Tel.: +33-1 69 08 79 25
Fax: +33-1 69 08 82 61
E-Mail: hinsen|at|llb.saclay.cea.fr
------------------------------------------------------------------------ 
-------

---

From: Torsten Becker <torsten.becker_at_iwr.uni-heidelberg.de>
Date: Tue, 13 Jul 2004 13:35:28 +0200 (CEST)

On Tue, 13 Jul 2004 victor_anisimov_at_comcast.net wrote:
> system. Thus we know how to perform "measurement". 

What you describe here is not a measurement. 
Given a measurable quantity represented by an Operator P, the outcome of a 
measurement will be one of the Eigenvalues p_i of P, not the mean value  
<W|P|W>. 
If |W_i> is an Eigenvector of P with Eigenvalue p_i, then <W|W_i> gives 
you the probability that your measurement yields p_i. 
Only after plenty of single measurements you can access  the mean value.

The 'measurement problem' in the Copenhagen Interpretation, as Konrad 
Hinsen wrote already, means that the measuring apparatus is not included 
in the system describtion given by the wavefunction |W>. In the 
Copenhageninterpretation the measuring apparatus is described in the 
framework of classical physics and measuring a system leads to a collaps 
of its wavefunction. 
'Collapse of the wavefunction` means that after a measurement that 
yielded p_i, the system is no longer in the state |W> but it 'collapsed' 
into the state |W_i>.

> The quantum problem, 
> results depending of their order. 

Energy and momentum usually do commute. They have to, otherwise energy and 
momentum would not both be conserved in physical processes. 
So the operator P usually commutes with the Hamiltonian H.

There are of course non-commuting operators like position and momentum and 
indeed that's the jist of QM. But it is not related to the measurement 
problem. 

************************************************************************
Torsten Becker                        Computational Molecular Biophysics   
                                      IWR, Universitaet Heidelberg 
+49-6221-54-8808 (office)             Im Neuenheimer Feld 368 
+49-0177-7273406 (mobile)             D-69120 Heidelberg; Germany

torsten.becker_at_iwr.uni-heidelberg.de ***********************************