{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T10:51:55Z","timestamp":1753872715140,"version":"3.41.2"},"reference-count":14,"publisher":"AIP Publishing","issue":"11","content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2008,11,1]]},"abstract":"<jats:p>Exact nonlinear stationary solutions of the one-dimensional Wigner and Wigner\u2013Poisson equations in the terms of the Wigner functions that depend not only on the energy but also on position are presented. In this way, the Bernstein\u2013Greene\u2013Kruskal modes of the classical plasma are adapted for the quantum formalism in the phase space. The solutions are constructed for the case of a quartic oscillator potential, as well as for the self-consistent Wigner\u2013Poisson case. Conditions for well-behaved physically meaningful equilibrium Wigner functions are discussed.<\/jats:p>","DOI":"10.1063\/1.3008047","type":"journal-article","created":{"date-parts":[[2008,11,6]],"date-time":"2008-11-06T01:19:06Z","timestamp":1225934346000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":7,"title":["Nonlinear stationary solutions of the Wigner and Wigner\u2013Poisson equations"],"prefix":"10.1063","volume":"15","author":[{"given":"F.","family":"Haas","sequence":"first","affiliation":[{"name":"Ruhr-Universit\u00e4t Bochum Institut f\u00fcr Theoretische Physik IV, , D-44780 Bochum, Germany"}]},{"given":"P. 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