Displaying similar documents to “Quasi-exact solvability of a hyperbolic intermolecular potential induced by an effective mass step.”

Eight exactly solvable complex potentials in Bender-Boettcher quantum mechanics

Znojil, Miloslav

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This is a readable review of recent work on non-Hermitian bound state problems with complex potentials. A particular example is the generalization of the harmonic oscillator with the potentials: V ( x ) = ω 2 2 x - 2 i β ω 2 - ω 2 . Other examples include complex generalizations of the Morse potential, the spiked radial harmonic potential, the Kratzer-Coulomb potential, the Rosen Morse oscillator and others. Instead of demanding Hermiticity H = H * the condition required is H = P T H P T where P changes the parity and T transforms i to...

Mean-Field Limit of Quantum Bose Gases and Nonlinear Hartree Equation

Jürg Fröhlich, Enno Lenzmann (2003-2004)

Séminaire Équations aux dérivées partielles

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We discuss the Hartree equation arising in the mean-field limit of large systems of bosons and explain its importance within the class of nonlinear Schrödinger equations. Of special interest to us is the Hartree equation with focusing nonlinearity (attractive two-body interactions). Rigorous results for the Hartree equation are presented concerning: 1) its derivation from the quantum theory of large systems of bosons, 2) existence and stability of Hartree solitons, and 3) its point-particle...