Quasi-exact solvability of a hyperbolic intermolecular potential induced by an effective mass step.

Schulze-Halberg, Axel

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Universal forms for one-dimensional quantum Hamiltonians: a comparison of the SUSY and the de la Peña factorization approaches.

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Power series techniques for a special Schrödinger operator and related difference equations.

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Eight exactly solvable complex potentials in Bender-Boettcher quantum mechanics

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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: $V (x) = \frac{ω^{2}}{2} {(x - \frac{2 i β}{ω})}^{2} - \frac{ω}{2} .$ 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

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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...