Re: Quantum physics study - Where to begin?


Gregory L. Hansen wrote:
> In article <dn04co$ig6$1@xxxxxxxxxxxxxxxxxxxxxx>,
> Ben Rudiak-Gould <br276deleteme@xxxxxxxxx> wrote:
> >Gregory L. Hansen wrote:
> >> Although introductory texts rarely say much about this, the big change
> >> from classical to quantum physics is the representation of state going
> >> from a vector in a phase space to a vector in a Hilbert space. That step
> >> does away with determinism and defines the wavefunction and the
> >> interpretation of it.
> >
> >I don't agree. That step can be factored into two smaller steps. In the
> >first half-step, you replace the vector in a phase space with a classical
> >probability distribution over vectors in the phase space. The set of
> >unnormalized distributions of this kind forms a Hilbert space whose
> >dimension is equal to the number of points in the original phase space. The
> >equivalence classes of such distributions, modulo normalization, are lines
> >through the origin. Determinism is lost, but the predictions of the theory
> >don't change; it's still classical.
> >
> >In the second half-step you simply replace the real probabilities with
> >complex amplitudes. That's where things become quantum. I think those
> >amplitudes are what quantum mechanics are really about. Some formulations of
> >quantum mechanics use a Hilbert space and others don't. Some have a collapse
> >postulate and others don't. Some quantum theories use particles and others
> >use waves. But the complex amplitudes are always there.
>
> Some interpretations of quantum mechanics have a collapse postulate and
> others don't. Some interpretations of quantum theories use particles and
> others use waves. There's a difference.
>
> I can't argue too strongly for one approach versus another. I haven't
> written the book yet, so my thoughts are rather incomplete. But I'd
> try to find smaller words to describe things like equivalence classes of
> distributions.
>
> I'm sort of divided on presenting pseudo-classical formulations like a
> classical probability distribution. The danger, I think, is that the
> student might grow up thinking, e.g., that the uncertainty principle
> represents a limit of our knowledge. I had thought of just staying away
> from psi(x) and plane waves entirely at first. Discuss vectors and bases,
> and generalize the concept, and go straight to bra-ket notation where we
> can show how a basis can be defined as mutually exclusive observable
> events like
>
> |psi> = (|left> + |right>)/sqrt(2)
>
> Focus on finite dimensions and the linear algebra. I wouldn't want to
> discuss <x|psi> until it can be shown how that's like the two-choice
> system above, but with more options. E.g.
>
> |psi> = a|x1> + b|x2> + c|x3> + d|x4>
>
> >
> >> You don't have to be able
> >> to actually find the hydrogen energy eigenfunctions given naught but a
> >> pencil and blank paper before you can claim some understanding of what
> >> quantum mechanics is all about. But you do have to know what an
> >> eigenfunction is.
> >
> >Well, it's a good idea to know what an eigenfunction is, but you certainly
> >don't have to. Eigenfunctions are peculiar to the operator formalism. If
>
> I would want to focus on the operator formalism. When quantum mechanics
> is presented as a wave mechanics with rules for calculating things like
>
> \int psi*(x) x psi(x) dx
>
> it becomes too easy to think of psi(x) as a classical wave, like a
> particle density or energy density. And that's not what it is. It
> obscures how |psi> is a vector and gives undue primacy to the position
> basis.

I'm inclined to agree, see...

http://groups.google.com/group/sci.physics.research/browse_frm/thread/8fde8c67205d1e74/e7cc277eac4fa234?q=tucker&rnum=72#e7cc277eac4fa234

it's the relativity of the energy change that matters, (IMO),
and basically, we're concerned with the emission and
absorption of photons, at least to start with that QT, QM,
WM, etc must first reconcile with GR, otherwise...just
a repetition.
Ken

.

Relevant Pages

  • Re: Quantum physics study - Where to begin?
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    (sci.physics)
  • Re: The time it takes to emit one photon
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