An exactly solvable model for a strongly spin-orbit-coupled nanowire quantum dot

In the presence of spin-orbit coupling, quantum models for semiconductor materials are generally not exactly solvable. As a result, understanding of the strong spin-orbit coupling effects in these systems remains poor. Here we develop an analytical method to solve the one-dimensional hard-wall quantum dot problem in the presence of strong spin-orbit coupling and magnetic field, which allows us to obtain exact eigenenergies and eigenstates of a single electron. With the help of the exact solution, we demonstrate some unique effects from the strong spin-orbit coupling in a semiconductor quantum dot, in particular the anisotropy of the electron g-factor and its tunability.