Journal ArticleDOI
Information theory and energy spectra.
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TLDR
The possibility of inferring energy spectra and their concomitant eigenstates on the basis of incomplete information concerning the system's ground state and the expectation values of a partially unknown Hamiltonian are examined and shown to be feasible.Abstract:
We examine the possibility of inferring energy spectra and their concomitant eigenstates on the basis of incomplete information concerning the system's ground state. In addition, the possibility of considering, as prior information, the expectation values of a partially unknown Hamiltonian also is examined and shown to be feasible.read more
Citations
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Journal ArticleDOI
Quantum information entropies and orthogonal polynomials
Jesús S. Dehesa,Andrei Martínez-Finkelshtein,Andrei Martínez-Finkelshtein,Jorge Sánchez-Ruiz,Jorge Sánchez-Ruiz +4 more
TL;DR: A survey of the present knowledge on the analytical determination of the Shannon information entropies for simple quantum systems: single-particle systems in central potentials can be found in this article.
Journal ArticleDOI
Asymptotic formula for the quantum entropy of position in energy eigenstates
TL;DR: In this paper, the information entropy in position space S Q of one-dimensional quantum systems in energy eigenstates, where S C is the position entropy corresponding to a microcanonical ensemble of analogous classical systems having the same energy, was derived.
Journal ArticleDOI
Logarithmic potential of Hermite polynomials and information entropies of the harmonic oscillator eigenstates
TL;DR: In this article, the information entropy in both position and momentum spaces for the nth stationary state of the one-dimensional quantum harmonic oscillator was derived for the Hermite polynomial Hn(x) at the zeros of Hnx.
Journal ArticleDOI
Ground state of the Hubbard model: a variational approach based on the maximum entropy principle
TL;DR: In this paper, a variational approach based on maximum entropy considerations is used to approximate the ground state of the Hubbard Hamiltonian, which is performed with a trial wave function, parameterized in terms of a small set of variables associated with the relevant correlation operators of the problem.
Book ChapterDOI
Information Theory and Quantum Wave Functions
TL;DR: In this article, a new scheme for the reconstruction and approximation of quantum wave functions is derived within the context of Information Theory, applied to the inference of the energy spectra and the pertinent eigen states of special hamiltonians from incomplete information concerning the system's ground state, and the development of an approximation for the ground state of a superconducting many-fermion model.
References
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Journal ArticleDOI
A mathematical theory of communication
TL;DR: This final installment of the paper considers the case where the signals or the messages or both are continuously variable, in contrast with the discrete nature assumed until now.
Journal ArticleDOI
Information Theory and Statistical Mechanics. II
TL;DR: In this article, the authors consider statistical mechanics as a form of statistical inference rather than as a physical theory, and show that the usual computational rules, starting with the determination of the partition function, are an immediate consequence of the maximum-entropy principle.
Journal ArticleDOI
Validity of many-body approximation methods for a solvable model: (I). Exact solutions and perturbation theory
TL;DR: In this paper, a model based on the bilinear products of creation and annihilation operators can be considered as generators of Lie groups and the problem of finding eigenvalues can be greatly simplified by the additional integrals of the motion which are present if the Hamiltonian is constructed so as to commute with invariants of the group.