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In theoretical physics, the logarithmic Schrödinger equation (sometimes abbreviated as LNSE or LogSE) is one of the nonlinear modifications of Schrödinger's equation. It is a classical wave equation with applications to extensions of quantum mechanics,〔I. Bialynicki-Birula and J. Mycielski, Annals Phys. 100, 62 (1976); Commun. Math. Phys. 44, 129 (1975); Phys. Scripta 20, 539 (1979).〕 quantum optics,〔H. Buljan, A. Šiber, M. Soljačić, T. Schwartz, M. Segev, and D. N. Christodoulides, Phys. Rev. E 68, 036607 (2003).〕 nuclear physics,〔E. F. Hefter, Phys. Rev. A 32, 1201 (1985).〕〔V. G. Kartavenko, K. A. Gridnev and W. Greiner, Int. J. Mod. Phys. E 7 (1998) 287.〕 transport and diffusion phenomena,〔S. De Martino, M. Falanga, C. Godano and G. Lauro, Europhys. Lett. 63, 472 (2003); S. De Martino and G. Lauro, in: Proceed. 12th Conference on WASCOM, 2003.〕〔T. Hansson, D. Anderson, and M. Lisak, Phys. Rev. A 80, 033819 (2009).〕 open quantum systems and information theory,〔K. Yasue, ''Quantum mechanics of nonconservative systems'', Annals Phys. 114 (1978) 479.〕〔N. A. Lemos, Phys. Lett. A 78 (1980) 239.〕〔J. D. Brasher, ''Nonlinear wave mechanics, information theory, and thermodynamics'', Int. J. Theor. Phys. 30 (1991) 979.〕〔D. Schuch, Phys. Rev. A 55, 935 (1997).〕〔M. P. Davidson, Nuov. Cim. B 116 (2001) 1291.〕〔J. L. Lopez, Phys. Rev. E. 69 (2004) 026110.〕 effective quantum gravity and physical vacuum models〔K. G. Zloshchastiev, ''Logarithmic nonlinearity in theories of quantum gravity: Origin of time and observational consequences'', Grav. Cosmol. 16 (2010) 288–297 (ArXiv:0906.4282 ).〕〔K. G. Zloshchastiev, ''Vacuum Cherenkov effect in logarithmic nonlinear quantum theory'', Phys. Lett. A 375 (2011) 2305–2308 (ArXiv:1003.0657 ).〕〔K. G. Zloshchastiev, ''Spontaneous symmetry breaking and mass generation as built-in phenomena in logarithmic nonlinear quantum theory'', Acta Phys. Polon. B 42 (2011) 261–292 (ArXiv:0912.4139 ).〕 and theory of superfluidity and Bose–Einstein condensation.〔A. V. Avdeenkov and K.G. Zloshchastiev, ''Quantum Bose liquids with logarithmic nonlinearity: Self-sustainability and emergence of spatial extent'', J. Phys. B: At. Mol. Opt. Phys. 44 (2011) 195303 (ArXiv:1108.0847 ).〕 Its relativistic version (with D'Alembertian instead of Laplacian and first-order time derivative) was first proposed by G. Rosen.〔G. Rosen, Phys. Rev. 183 (1969) 1186.〕 It is an example of an integrable model. == The equation == The logarithmic Schrödinger equation is the partial differential equation. In mathematics and mathematical physics one often uses its dimensionless form: : for the complex-valued function . The relativistic version of this equation can be obtained by replacing the derivative operator with the D'Alembertian, similarly to the Klein–Gordon equation. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Logarithmic Schrödinger equation」の詳細全文を読む スポンサード リンク
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