- #1

cgk

Science Advisor

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## Main Question or Discussion Point

...that's the title of a recent communication in the Journal of Chemical Physics[1] (as communication it is free access to everyone):

http://jcp.aip.org/resource/1/jcpsa6/v136/i3/p031102_s1 [Broken]

The authors perform some rather clever looking algebraic transformations and arrive at a formulation of nonrelativistic spinless QM (without fermionic or bosonic symmetry constraints, though) which looks a lot like a classical Hamilton-Jacobi formulation of mechanics with one additional quantum coordinate/momentum pair (additionally to the classical position/momentum coordinates) for each particle. That's basically the hidden variable, as far as I understand.

I was wondering if any of you had an opinion on this approach, especially the experts on QM interpretations. I am myself not quite sure what to make of that. On the one hand it does look very clever and leads to an entirely real formulation (i.e., no complex numbers) of QM without wave functions and with a clear action principle. On the other hand, it looks a bit like just replacing the N-dimensional complex Schroedinger equation by a 2N-dimensional set of real differential equations. The chief advantage seems to be that the latter is easier to combine with classical approximations and easier to integrate numerically. But is this also a novel way of looking at things? Is there more to it? (The authors seems to think so and make some rather grand claims normally not found in J. Chem. Phys.). Any opinions welcome.

[1]: If you are concerned about the journal: J. Chem. Phys. is highly respected and the #1 journal for chemical physics and many parts of molecular physics---in particular for all kinds of numerical quantum dynamics and quantum mechanics applied to real atomic and molecular systems. If the authors had actually found a reformulation of QM which is helpful for numerical computations, it would make

http://jcp.aip.org/resource/1/jcpsa6/v136/i3/p031102_s1 [Broken]

The authors perform some rather clever looking algebraic transformations and arrive at a formulation of nonrelativistic spinless QM (without fermionic or bosonic symmetry constraints, though) which looks a lot like a classical Hamilton-Jacobi formulation of mechanics with one additional quantum coordinate/momentum pair (additionally to the classical position/momentum coordinates) for each particle. That's basically the hidden variable, as far as I understand.

I was wondering if any of you had an opinion on this approach, especially the experts on QM interpretations. I am myself not quite sure what to make of that. On the one hand it does look very clever and leads to an entirely real formulation (i.e., no complex numbers) of QM without wave functions and with a clear action principle. On the other hand, it looks a bit like just replacing the N-dimensional complex Schroedinger equation by a 2N-dimensional set of real differential equations. The chief advantage seems to be that the latter is easier to combine with classical approximations and easier to integrate numerically. But is this also a novel way of looking at things? Is there more to it? (The authors seems to think so and make some rather grand claims normally not found in J. Chem. Phys.). Any opinions welcome.

[1]: If you are concerned about the journal: J. Chem. Phys. is highly respected and the #1 journal for chemical physics and many parts of molecular physics---in particular for all kinds of numerical quantum dynamics and quantum mechanics applied to real atomic and molecular systems. If the authors had actually found a reformulation of QM which is helpful for numerical computations, it would make

*a lot*of sense to publish it there first, because that is the journal the people read who would likely use it.
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