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• W2873796054 abstract "The nonlinear logarithmic Schrödinger equation (log SE) appears in many branches of fundamental physics, ranging from macroscopic superfluids to quantum gravity. We consider here a model problem, in which the log SE includes an attractive Coulomb interaction. We derive an analytical solution for the ground state energy and wave function as a function of the strength of the logarithmic interaction. We develop an iterative finite element method to solve the Coulombic log SE for the spherically symmetric states. The ground state results agree with the exact solution to better than one part in 1010. The excited states (n>1) are converged to better than one part in 108. We also construct a remarkably simple variational wave function, consisting of a sum of Gaussons with n free parameters. One can obtain an approximation to the energy and wave function that is in good agreement with the finite element results. Although the Coulomb problem is interesting in its own right, the iterative finite element method and the variational Gausson basis approach can be applied to any central force Hamiltonian." @default.
• W2873796054 created "2018-07-19" @default.
• W2873796054 creator A5016598068 @default.
• W2873796054 creator A5047221356 @default.
• W2873796054 date "2018-07-24" @default.
• W2873796054 modified "2023-09-27" @default.
• W2873796054 title "Solution of the logarithmic Schrödinger equation with a Coulomb potential" @default.
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• W2873796054 doi "https://doi.org/10.1088/2399-6528/aad302" @default.
• W2873796054 hasPublicationYear "2018" @default.
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