The Cramér-Rao, Fisher-Shannon and LMC shape complexity measures have been recently shown to play a relevant role to study the internal disorder of finite many-body systems (e.g., atoms, molecules, nuclei). They highlight amongst the bunch of complexities appeared in the literature by their mathematical simplicity and transparent physical interpretation. They are composed by two spreading measures (variance, Fisher information and Shannon entropies) of the single-particle probability density of the systems. Here we discuss the physico-mathematical knowledge of these two-component complexities for hydrogenic systems with standard ( $D = 3$ ) and non-standard dimensionalities. These systems include not only the hydrogen atom and its isoelectronic series but also a large diversity of quantum systems such as, e.g. exotic atoms, antimatter atoms, some qubits systems and Rydberg atoms, ions and molecules.The Cramér-Rao, Fisher-Shannon and LMC shape complexity measures have been recently shown to play a relevant role to study the internal disorder of finite many-body systems (e.g., atoms, molecules, nuclei). They highlight amongst the bunch of complexities appeared in the literature by their mathematical simplicity and transparent physical interpretation. They are composed by two spreading measures (variance, Fisher information and Shannon entropies) of the single-particle probability density of the systems. Here we discuss the physico-mathematical knowledge of these two-component complexities for hydrogenic systems with standard ($D = 3$) and non-standard dimensionalities. These systems include not only the hydrogen atom and its isoelectronic series but also a large diversity of quantum systems such as, e.g. exotic atoms, antimatter atoms, some qubits systems and Rydberg atoms, ions and molecules.

arXiv:1305.4041International Journal of Applied Mathematics & Statistics/International journal of applied mathematics and statisticsMay 17, 20131 citation

Quantum Mechanics in Mathematics, Chemistry, and Physics

Springer eBooksJan 1, 198159 citations

Squeezed coherent states and the one-dimensional Morse quantum system

Maia N Angelova, A Hertz, Véronique Hussin

The Morse potential one-dimensional quantum system is a realistic model for studying vibrations of atoms in a diatomic molecule. This system is very close to the harmonic oscillator one. We thus propose a construction of squeezed coherent states similar to the one of the harmonic oscillator using ladder operators. The properties of these states are analysed with respect to the localization in position, minimal Heisenberg uncertainty relation, the statistical properties and illustrated with examples using the finite number of states in a well-known diatomic molecule. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’.The Morse potential one-dimensional quantum system is a realistic model for studying vibrations of atoms in a diatomic molecule. This system is very close to the harmonic oscillator one. We thus propose a construction of squeezed coherent states similar to the one of the harmonic oscillator using ladder operators. The properties of these states are analysed with respect to the localization in position, minimal Heisenberg uncertainty relation, the statistical properties and illustrated with examples using the finite number of states in a well-known diatomic molecule. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’.

arXiv:1111.1974Journal of Physics A Mathematical and TheoreticalMay 30, 201230 citations

Quantum Mathematical Physics

Felix Finster, Johannes Kleiner, Christian Röken +1 more

Springer eBooksJan 1, 201617 citations

Quantum mechanics of atoms and molecules

Walter E Thirring, Evans M. Harrell

Springer eBooksJan 1, 1981144 citations

D = 3

) and non-standard dimensionalities. These systems include not only the hydrogen atom and its isoelectronic series but also a large diversity of quantum systems such as, e.g. exotic atoms, antimatter atoms, some qubits systems and Rydberg atoms, ions and molecules.