periodic behavior
Electronic Shells in Large Quantum Dots
https://doi.org/10.1007/978-94-009-0211-4_4
behavior
https://scigraph.springernature.com/explorer/license/
planetary motion
orbit
Bloch
approach
atoms
chaotic systems
semiclassical model
quantization
mechanical picture
1996-01-01
cases
atomic clusters
quantum principles
2022-10-01T06:59
shell structure
number
years
chaotic dynamics
false
small particles
density
physical phenomena
groups of elements
Balian
results
delight
chapter
physicists
emphasis
Heisenberg’s matrix mechanics
et al
dynamics
89-110
density of states
explanation
shell
failure
clusters
rudiments
chapters
Bohr
system
Sommerfeld
Gutzwiller
interest
solution
nucleus
equations
mechanics
quantum dots
al
phenomenon
electronic shells
chemical properties
study of nuclei
periodic systems
molecules
number of particles
success
variation
regularity
1996
quantum behavior
model
matrix mechanics
description
dots
state
extent
group
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’s 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)).
experimental discovery
classical chaotic dynamics
first explanation
advanced solutions
motion
article
work
study
shell behavior
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picture
quantum mechanics
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discovery
regular variation
today
spectral density
quantitative predictions
principles
large quantum dots
quantal behavior
mingling
similar chemical properties
terms
motion approach
prediction
properties
century
shell model
periodic orbits
complex quantum systems
appearance
helium atoms
Nishioka et al
prime example
nuclear shell model
discreteness
quantum systems
Niels Bohr
experimental results
structure
supershell structure
elements
particles
wave equation
Springer Nature
Persson
M.
Department of Physics, Chalmers University of Technology, S-96012, Gothenburg, Sweden
Department of Physics, Chalmers University of Technology, S-96012, Gothenburg, Sweden
Lindelof
P. E.
Hullmann
P.
Physical Sciences
Springer Nature - SN SciGraph project
Atomic, Molecular, Nuclear, Particle and Plasma Physics
978-94-009-0211-4
978-94-010-6579-5
Large Clusters of Atoms and Molecules
Reimann
S. M.
doi
10.1007/978-94-009-0211-4_4
dimensions_id
pub.1037355485
Institute for Theoretical Physics, University of Regensburg, D-9304O, Regensburg, Germany
Institute for Theoretical Physics, University of Regensburg, D-9304O, Regensburg, Germany
P.
Bøggild
The Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, DK-2100, Copenhagen, Denmark
The Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, DK-2100, Copenhagen, Denmark
T. P.
Martin