Information and quantum theories: an analysis in one-dimensional systems

@article{Nascimento2020InformationAQ,
  title={Information and quantum theories: an analysis in one-dimensional systems},
  author={Wallas S. Nascimento and Marcos M. de Almeida and Frederico Vasconcellos Prudente},
  journal={European Journal of Physics},
  year={2020}
}
We pedagogically present the information theory as originally established, explaining its essential ideas and paying attention to the expression employed to measure the amount of information. Also we discussed relationships between information and quantum theories. In this context we determined the information entropies on position, $S_x$, and momentum, $S_p$, spaces, besides the entropy sum $S_t$. Here, we use the modified entropic expressions that are dimensionally consistent. We provide… 
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References

SHOWING 1-10 OF 52 REFERENCES
Thermodynamics and Statistical Mechanics
Foreword.- Preface.- Thermodynamics: Equilibrium and State Quantities.- The Laws of Thermodynamics.- Phase Transitions and Chemical Reactions.- Thermodynamic Potentials.- Statistical Mechanics:
A mathematical theory of communication
In this final installment of the paper we consider the case where the signals or the messages or both are continuously variable, in contrast with the discrete nature assumed until now. To a
Uncertainty relations for information entropy in wave mechanics
New uncertainty relations in quantum mechanics are derived. They express restrictions imposed by quantum theory on probability distributions of canonically conjugate variables in terms of
Some novel characteristics of atomic information entropies.
TLDR
This study for atoms in their ground states, using wave functions of single-zeta, double-Zeta, and near-Hartree-Fock quality, unearths a startling feature that the entropy sum, S ρ +S γ, increases with an enhancement in the ground-state wave-function quality.
The mathematical theory of communication
TLDR
This commemorative reprinting of The Mathematical Theory of Communication, published originally as a paper on communication theory more than fifty years ago, is released.
Fisher information for endohedrally confined hydrogen atom
Stability after confinement of the H atom
Role of the cut-off function for the ground state variational wavefunction of the hydrogen atom confined by a hard sphere
A variational treatment of the hydrogen atom in its ground state, enclosed by a hard spherical cavity of radius Rc , is developed by considering the ansatz wavefunction as the product of the
...
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