"https://scigraph.springernature.com/explorer/license/" .
"electronic shells" .
"properties" .
"Niels Bohr" .
"century" .
"P. E." .
"shell structure" .
"large quantum dots" .
_:N3baf7094d5534833bacd7954ad2a585b .
"Bloch" .
_:N4d7ceea071384d8388559738130582ab .
"atoms" .
"complex quantum systems" .
"particles" .
"regular variation" .
"discreteness" .
.
"The quantum mechanical discreteness in the properties of small particles manifests itself over and over again in the study of nuclei, atoms, molecules and atomic clusters. As a system grows larger, its behavior can be understood in terms of semi classical instead of quantum mechanics. However, rudiments of quantal behavior may be observed even in cases, where the microscopic discreteness is extinguished, appearing as a slow but regular variation of the spectral density with the number of particles. We often refer to this structure of the density of states as shells. The nuclear shell model is perhaps the most extraordinary in its beauty and regularity. The periodic system of elements is the most widely appreciated example of shell behavior, where the shells are reflected in the appearance of eight groups of elements showing similar chemical properties. A first explanation of this periodic behavior was given by Niels Bohr in his famous three articles from 1913 with an ingenious mingling of classical planetary motion and the quantum principle, which was further developed by Bohr and Sommerfeld. Due to its failure to explain more complex quantum systems, e.g. the helium atom, the semiclassical model was abandoned many years ago and replaced by highly advanced solutions to the wave equation and Heisenberg\u2019s matrix mechanics early in this century. Many physicists, nevertheless, still find delight in intuitive, mechanical pictures of physical phenomena exhibiting quantum behavior. Applying the planetary motion approach of Bohr and Sommerfeld to quantum phenomena may not be considered appropriate and does often fail, particularly for systems exhibiting classical chaotic dynamics. Over the last 25 years this approach to the description of quantum systems has gained increased interest due to work by Gutzwiller (1991) with an emphasis on the quantization of classically chaotic systems. He developed it to the extent that we can use it to make quantitative predictions and compare to experimental results. The shell structure in atomic clusters (Knight et al., 1984), and in particular the experimental discovery of the supershell structure (Pedersen et al., 1991) predicted by Balian and Bloch (1972) and Nishioka et al (1990) is today a prime example of the success of the quantization of periodic orbits (for a description of periodic orbit theory see the contribution in these proceedings by M. Brack et al. (1995))." .
"et al" .
"number" .
"experimental discovery" .
"delight" .
.
.
_:N0869b7d3c4bd41df8cb088e6f0d69e65 .
"quantization" .
"rudiments" .
_:N6ddcf171efb0448abf69ddf3ffae487b "pub.1037355485" .
_:N3baf7094d5534833bacd7954ad2a585b _:Nf434c74940a74a83acc176167a9f6d15 .
_:Nd864ec2b600a4570b6c211ecad355d8d "978-94-009-0211-4" .
_:N4d7ceea071384d8388559738130582ab .
"mingling" .
"P." .
_:Nd864ec2b600a4570b6c211ecad355d8d "978-94-010-6579-5" .
_:N583338498cb74b2bbd4b28fd4392593b .
.
"solution" .
"extent" .
"Heisenberg\u2019s matrix mechanics" .
"nuclear shell model" .
"emphasis" .
"orbit" .
"quantum mechanics" .
_:N4b3a7ab8f8564d358cea1aeaf4278eea .
"The Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, DK-2100, Copenhagen, Denmark" .
_:N5089f4bed43443b9b33e05649a063eee .
"planetary motion" .
"mechanical picture" .
_:N6ddcf171efb0448abf69ddf3ffae487b .
"density" .
"semiclassical model" .
"advanced solutions" .
_:Nd864ec2b600a4570b6c211ecad355d8d "Large Clusters of Atoms and Molecules" .
.
.
"1996" .
"phenomenon" .
"appearance" .
"Lindelof" .
_:Nd864ec2b600a4570b6c211ecad355d8d .
_:N28b2da36bb604031a0632dbecac2d134 .
.
"success" .
_:N28b2da36bb604031a0632dbecac2d134 .
"model" .
"behavior" .
"first explanation" .
"quantum behavior" .
"The Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, DK-2100, Copenhagen, Denmark" .
"dynamics" .
"shell model" .
"shell behavior" .
"quantal behavior" .
"al" .
.
.
"picture" .
"quantum dots" .
"atomic clusters" .
.
"similar chemical properties" .
.
"physical phenomena" .
_:Nf434c74940a74a83acc176167a9f6d15 "Martin" .
"discovery" .
.
"Electronic Shells in Large Quantum Dots" .
"chaotic dynamics" .
"elements" .
.
"prime example" .
_:N4d7ceea071384d8388559738130582ab "10.1007/978-94-009-0211-4_4" .
_:N4d7ceea071384d8388559738130582ab "doi" .
"periodic orbits" .
"study" .
"molecules" .
.
"Gutzwiller" .
"Physical Sciences" .
"article" .
.
"density of states" .
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.
"terms" .
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.
"motion approach" .
_:N3baf7094d5534833bacd7954ad2a585b .
"Bohr" .
.
"spectral density" .
"Reimann" .
"motion" .
"nucleus" .
"P." .
"Department of Physics, Chalmers University of Technology, S-96012, Gothenburg, Sweden" .
.
"approach" .
"chapters" .
"chemical properties" .
"89-110" .