Harris sheet solution for magnetized quantum plasmas

We construct an infinite family of one-dimensional equilibrium solutions for purely magnetized quantum plasmas described by the quantum hydrodynamic model. The equilibria depends on the solution of a third-order ordinary differential equation, which is written in terms of two free functions. One of these free functions is associated to the magnetic field configuration, while the other is specified by an equation of state. The case of a Harris sheet type magnetic field, together with an isothermal distribution, is treated in detail. In contrast to the classical Harris sheet solution, the quantum case exhibits an oscillatory pattern for the density.