The Fourier-symmetric quantum-Hamiltonian operator $H = v|p| + F|x|$
(with an immediate relevance in physics of antiferromagnetic spin
chains and spinons) is defined and studied. Several interesting
mathematical features (e.g., asymptotics) of the model are
discussed. Its numerical (i.e., discretization-plus-diagonalization)
solutions are shown to agree with their quasi-classical
approximations.


MR2660139 Greiter, Martin, On the linear-dispersion --
 linear-potential quantum oscillator. Ann. Physics 325 (2010),
no. 7, 1349--1358. 81Q05