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It should be emphasized that these are not uncommon examples
of atomic or planetary nebula morphologies. To the contrary, they are THE MOST
COMMON SHAPES for both types of system: spheriod, bipolar "propeller", caps,
"butterfly", toroid, sphere-within-a-sphere, etc. It is not necessary to choose rare examples in order to achieve isomorphism. These are archetypal shapes for the atomic and stellar scale systems. | ||||
A. ATOMIC MORPHOLOGY |
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1. The far left atomic scale shapes are visual depictions of electron probability densities
for the simplest atom, hydrogen, in its lowest energy state and a few excited states. Usually
these probability densities are interpreted as abstract probabilities for finding a point-like
electron at a given place. Another interpretation (one not favored by most physicists, though
Schrodinger himself favored it) is as follows. When electrons become bound to an atom, their
mass is spread out into these shapes. What are called abstract probability density distributions
are really distributions of the physical mass of the electron for a given energy state. 2. Pictoral examples of these density distributions can be found in the following sources: |
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(a.) H.E. White, Physical Review, Vol. 37, 1931 (p. 1419 and p. 1423).
[These images are the widely acknowledged classics] (b.)R. Eisberg and R. Resnick, Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles (2nd Ed.), John Wiley, New York, 1985 (p.251). This Material is used by permission of John Wiley & Sons, Inc. Copyright (R) 1985, John Wiley & Sons, Inc. | ||
B. PLANETARY NEBULA MORPHOLOGY |
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1. It should be kept in mind that planetary nebulae are created when their central stars somewhat
violently eject their outer shells. Some loss of the pre-existing symmetry and detailed morphology
can be expected for these expanding structures. 2. Excellent collections of planetary nebula images can be found on the internet at www.blackskies.com/links. 3. For a basic discussion of what planetary nebula systems are, see www.astro.washington.edu/balick/WFPC2. 4. As mentioned above, the origin and maintenance of planetary nebula morphologies are still considered to be unsolved problems by professional astrophysicists. 5. The planetary nebula images shown above are recreated from images found on the web, or published in books and journals. |
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More information, images, matches, links, etc. are coming, as
well as a discussion of how this example of self-similarity (parts resemble "whole") was
predicted. For a review of the latter see:
http://www.amherst.edu/~rloldershaw/ |
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