Science > Physics > The Missing "Review Energy" Keyword Papers in arXiv/Front 3.1: A Danish-German Simultaneous Review and Un-Review
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Science > Physics |
| User: |
"OsherD" |
| Date: |
13 Dec 2005 02:14:48 PM |
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The Missing "Review Energy" Keyword Papers in arXiv/Front 3.1: A Danish-German Simultaneous Review and Un-Review |
From Osher Doctorow
Dahl and Schleich (2001) (see part 3 or 3.0 of this thread) divide
kinetic energy into radial and angular parts differently in the
wavefunction picture and the Weyl-Wigner phase-space picture. The
separation of kinetic energy of a particle moving in a central field
into an angular part and a radial part was previously tacticly assumed
to be only sensibly described by the wavefunction picture. However,
the separation in the phase-space picture is equally well defined (tied
to the Weyl correspondence rule) and in contrast to the wavefront
picture it reveals the correlation between directions of the position
and momentum vectors, respectively r and p, which correlation can't be
discussed or analyzed in the wavefunction picture.
The kinetic energy of the ground state of the hydrogen atom (one of two
examples discussed in the paper) turns out to be purely radial in the
wavefunction picture and purely angular in the phase-space picture,
enabling our use of different intuitive abilities. In the wavefunction
picture, angular momentum for example mainly refers to behavior of
state under rotations, while in the phase-space picture it also refers
to the correlation between directions of r and p, and both are needed
to properly understand the quantum systems.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: The Missing "Review Energy" Keyword Papers in arXiv/Front 3.1: A Danish-German Simultaneous Review and Un-Review |
13 Dec 2005 02:29:30 PM |
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From Osher Doctorow
The Wigner function is defined as:
1) W(r, p) = k^D I[w*(r-r' /2)w(r + r' /2) exp(-ip.r' /h)]dr'
where k = (1/(2pi h)) and 2D is the dimension and I[...]dr' is the
integral on 2D-dimensional (r, p) phase space. It is normalized to
II[W(r, p)drdp = 1 with particle density rho(r) and momentum density
PI(p) as marginal densities:
2) rho(r) = I[W(r, p)]dp
3) PI(p) = I[W(r,p)]dr
The two eigenstates of the position-vector operator correspond to the
eigenvalues r - r' /2 and r + r' /2.
Osher Doctorow
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