Lobachevskii Journal of Mathematics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Lobachevskii J. Math.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Lobachevskii Journal of Mathematics, 2006, Volume 23, Pages 29–56 (Mi ljm16)  

Maximum Entropy Wave functions

P. K. Jakobsen, V. V. Lychagin

University of Tromsø
References:
Abstract: In this paper we use the classical Maximum Entropy principle to define maximum entropy wave functions. These are wave functions that maximize the entropy among all wave functions satisfying a finite set of constraints in the form of expectation values. This lead to a nonlinear equation for the wave function that reduce to the usual stationary Schrödinger equation if the energy is the only constraint and the value of the constraint is an eigenvalue. We discuss the extension of the thermodynamical formalism to this case and apply our general formalism to several simple quantum systems, the two-level atom, the particle in a box, the free particle and the Harmonic Oscillator and compare with the results obtained by applying the usual von Neumann quantum statistical method to the same systems.
Keywords: Maximum entropy principle, quantum mechanics, wavefunctions, probability theory, density matrix.
Received: 28.06.2006
Bibliographic databases:
Language: English
Citation: P. K. Jakobsen, V. V. Lychagin, “Maximum Entropy Wave functions”, Lobachevskii J. Math., 23 (2006), 29–56
Citation in format AMSBIB
\Bibitem{JakLyc06}
\by P.~K.~Jakobsen, V.~V.~Lychagin
\paper Maximum Entropy Wave functions
\jour Lobachevskii J. Math.
\yr 2006
\vol 23
\pages 29--56
\mathnet{http://mi.mathnet.ru/ljm16}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2293364}
\zmath{https://zbmath.org/?q=an:1111.82025}
Linking options:
  • https://www.mathnet.ru/eng/ljm16
  • https://www.mathnet.ru/eng/ljm/v23/p29
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Lobachevskii Journal of Mathematics
    Statistics & downloads:
    Abstract page:429
    Full-text PDF :138
    References:40
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024