Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Ground-state wave functions and maximum entropy

N. Canosa, Angel Ricardo Plastino, R. Rossignoli

Published Jul 1, 1989• 53 citations
Publisher

Abstract

A modified version of the maximum-entropy principle is applied to distributions associated with special quantum states. In this way, it becomes feasible to make statistical inferences concerning the ground-state wave function and the associated potential from the sole knowledge of a few relevant mean values. The scheme is illustrated for the case of anharmonic and Morse potentials and yields excellent results.

DOI
10.1103/physreva.40.519

Related papers

Maximum-entropy principle and neural networks that learn to construct approximate wave functions

Luis Anibal Diambra, Angel Ricardo Plastino

By recourse to a maximum-entropy-based method for the training of perceptrons, we show that an appropriately prepared network is able to construct approximate ground state wave functions of good quality with the sole knowledge of a few expectation values, even if nothing is known concerning the interaction potential. \textcopyright{} 1996 The American Physical Society.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Jan 1, 1996•6 citations

Information Theory and Statistical Mechanics Revisited

Jian Zhou

We derive Bose-Einstein statistics and Fermi-Dirac statistics by Principle of Maximum Entropy applied to two families of entropy functions different from the Boltzmann-Gibbs-Shannon entropy. These entropy functions are identified with special cases of modified Naudts' $ϕ$-entropy.

arXiv:1604.08739•Apr 29, 2016•4 citations

Maximum-entropy approach to critical phenomena in ground states of finite systems

Liliana Arrachea, N. Canosa, Angelo Plastino +2 more

A scheme for detecting signatures of phase transitions associated with pure quantum states, from the knowledge of a limited set of expectation values, is introduced. An accurate prediction of critical regions in ground states of systems with a finite number of particles is obtained.

Physical Review A•May 1, 1992•22 citations

Quantum entanglement and the maximum-entropy states from the Jaynes principle

A. K. Rajagopal

We show that the Jaynes principle is indeed a proper inference scheme when applied to compound systems and will correctly produce the entangled maximum entropy states compatible with appropriate data. This is shown in a particular example considered recently by Horodecki et al. [Phys. Rev. A 59, 1799 (1999)], by including the dispersion of the entanglement along with its mean value as constraints and an application of the uncertainty principle. We also construct a ``thermodynamiclike'' description of the entanglement arising out of the maximum entropy principle.

arXiv:quant-ph/9903083•Physical Review A•Dec 1, 1999•14 citations

Maximum entropy approach to Schrödinger's radial equation

F. Garcías, M. Casas, Angel Ricardo Plastino

Abstract From the sole knowledge (at a finite number of points) of the numerical values of the potential V(r) corresponding to Schrödinger's radial equation, it is found that recourse to Information Theory (IT) concepts allows one to infer the pertinent wave functions (and eigenvalues) without attempting to solve the concomitant differential equation. Moreover, the underlying IT ideas allow for an analytical treatment that yields exact wave functions of the maximum (quantal) entropy form in a number of cases of interest.

Annalen der Physik•Jan 1, 1995•3 citations

Ground State Quantum Oscillator Density as an Entropy Maximum

Francesco R. Ruggeri

Classical statistical mechanical density maximizes entropy subject to constraints i.e. one has the Maxwell-Boltzmann (MB) distribution P(x)P(p) proportional to exp(- pp/2mT - V(x)/T). Quantum mechanics is also a statistical theory, but it is not based on the maximization of entropy. Rather it is based on a conditional probability P(p/x) = a(p)exp(ipx)/W(x) where W(x) =wavefunction = Sum over p a(p)exp(ipx) such that: Sum over p pp/2m P(p/x) + V(x) = E (bound states). As a result, it has classical densities P(x)=W(x)W(x) and P(p)=a(p)a(p), but these in general do not maximize entropy and so do not match the MB distribution. There is a special case, however, namely the ground state oscillator for which the quantum mechanical results P(x) and P(p) are both Gaussians. It is shown in (1) that for a fixed variance, a Gaussian maximizes entropy. Thus, the MB scenario must be a Gaussian for an oscillator as it is, but the quantum result is also a Gaussian and so matches the classical statistical mechanical result. In this note, we show that the time-independent Schrodinger equation collapses to the equality situation in Heisenberg’s uncertainty principle, suggesting that the solution also represents maximum entropy.

•Apr 29, 2022•0 citations
A modified version of the maximum-entropy principle is applied to distributions associated with special quantum states. In this way, it becomes feasible to make statistical inferences concerning the ground-state wave function and the associated potential from the sole knowledge of a few relevant mean values. The scheme is illustrated for the case of anharmonic and Morse potentials and yields excellent results.
We derive Bose-Einstein statistics and Fermi-Dirac statistics by Principle of Maximum Entropy applied to two families of entropy functions different from the Boltzmann-Gibbs-Shannon entropy. These entropy functions are identified with special cases of modified Naudts' ϕϕϕ-entropy.
We show that the Jaynes principle is indeed a proper inference scheme when applied to compound systems and will correctly produce the entangled maximum entropy states compatible with appropriate data. This is shown in a particular example considered recently by Horodecki et al. [Phys. Rev. A 59, 1799 (1999)], by including the dispersion of the entanglement along with its mean value as constraints and an application of the uncertainty principle. We also construct a ``thermodynamiclike'' description of the entanglement arising out of the maximum entropy principle.
Abstract From the sole knowledge (at a finite number of points) of the numerical values of the potential V(r) corresponding to Schrödinger's radial equation, it is found that recourse to Information Theory (IT) concepts allows one to infer the pertinent wave functions (and eigenvalues) without attempting to solve the concomitant differential equation. Moreover, the underlying IT ideas allow for an analytical treatment that yields exact wave functions of the maximum (quantal) entropy form in a number of cases of interest.
Classical statistical mechanical density maximizes entropy subject to constraints i.e. one has the Maxwell-Boltzmann (MB) distribution P(x)P(p) proportional to exp(- pp/2mT - V(x)/T). Quantum mechanics is also a statistical theory, but it is not based on the maximization of entropy. Rather it is based on a conditional probability P(p/x) = a(p)exp(ipx)/W(x) where W(x) =wavefunction = Sum over p a(p)exp(ipx) such that: Sum over p pp/2m P(p/x) + V(x) = E (bound states). As a result, it has classical densities P(x)=W(x)W(x) and P(p)=a(p)a(p), but these in general do not maximize entropy and so do not match the MB distribution. There is a special case, however, namely the ground state oscillator for which the quantum mechanical results P(x) and P(p) are both Gaussians. It is shown in (1) that for a fixed variance, a Gaussian maximizes entropy. Thus, the MB scenario must be a Gaussian for an oscillator as it is, but the quantum result is also a Gaussian and so matches the classical statistical mechanical result. In this note, we show that the time-independent Schrodinger equation collapses to the equality situation in Heisenberg’s uncertainty principle, suggesting that the solution also represents maximum entropy.