Re: orbitals, flowers, quantum puzzlement;

> For isolated atoms, rho is spherically symmetric, giving symmetric
> shapes. For molecules, rho is in fact a function of the coordinates of
> all nuclei involved, and there is no longer any reason to have more
> symmetry than the symmetry of the configuration of nuclei has, which is
> very little and often none.
>

Hmm. OK. But what determines the relative positions of the nuclei which are
each in and of themselves, basically spherically symmetric?

> The shape of molecules is therefore mainly determined by the geometry
> of the positions of the nuclei. In equilibrium, these arrange
> themselves such that the potential energy, i.e., the smallest
> eigenvalue of the Hamiltonian operator for the electrons is minimal
> among all other positions (or at least a local minimum from which a
> deeper lying state is very difficult to reach). A few years ago,
> I wrote a survey of molecular modeling of proteins, the largest
> molecules in nature (apart from crystals, which are essentially
> molecules of macroscopic size):
> A. Neumaier,
> Molecular modeling of proteins and mathematical prediction of
> protein structure,
> SIAM Review 39 (1997), 407-460.
> http://www.mat.univie.ac.at/~neum/papers/physpapers.html#protein
>
> Finally, snow flakes, crystals and flowers are so large objects that
> the underlying microscopic structure hardly matters (except for a few
> material properties).
>
>> I am begining the think that I (like Lee Smolin) do not understand QM; I
>> wonder if quantum mechanics as taught is not conceptually coherent. There
>> is
>> a definite mathematical structure (rigged Hilbert spaces etc.) but the
>> application is piecemeal and involves equivocations and hand waving.
>
> This is just because of lack of lecture time (or preparation time)
> in courses, and lack of writing time for books...
>
>> Little puzzles like the one I give here always have answers but those
>> answers apply ontological strategies that seem ad hoc and directed only
>> to
>> the particular puzzle at hand.
>
> With more reading and experience, things get easier and the grand
> picture emerges. But research on putting the picture together is not
> rewarded in the current scientific tradition, so people rather work
> on deep and hard isolated questions for which they can earn phd's and
> publications, rather than on the whole picture, which convinces
> (and is publishable as a book) only when it is completed.
>
> My theoretical physics FAQ at
> http://www.mat.univie.ac.at/~neum/physics-faq.txt
> is intended to bridge the gap in some ways; perhaps it will
> become a book one day in the far future...
>
> Arnold Neumaier
>

.

Relevant Pages

  • Re: Is Perfect Reversibility A Myth?
    ... Ammonia inversion is reversible, but is it symmetric? ... Theory of fundamental symmetry principles in chemical reactions ... and of parity violation in polyatomic molecules" ... Hund's paradox concerning the enantiomeric state of chiral molecules ...
    (sci.physics.research)
  • Re: orbitals, flowers, quantum puzzlement;
    ... For molecules, rho is in fact a function of the coordinates of all nuclei involved, and there is no longer any reason to have more symmetry than the symmetry of the configuration of nuclei has, which is very little and often none. ... There are several local minima in the potential energy surface, ... There may also be peculiarities due to surface crossing, where the Born-Oppenheimer approximation breaks down. ...
    (sci.physics.research)
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