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Two interacting electrons in a magnetic field: comparison of semiclassical, quantum, and variational solutions
interacting electrons time-dependent variational principle
2010/10/27
The quantum mechanical many-body problem is rarely analytically solvable. One notable exception is the case of two electrons interacting via a Coulomb potential in a uniform magnetic field. The motion...
Increasing variational solutions for a nonlinear $p$-laplace equation without growth conditions
variational solutions nonlinear $p$-laplace equation
2010/12/7
By means of a recent variational technique, we prove the existence of radially monotone solutions to a class of nonlinear problems involving the p-Laplace operator. No subcriticality condition (in the...