  Recently, we have suggested Fermi-liquid - non-Fermi-liquid angular
crossovers which may exist in quasi-one-dimensional (Q1D)conductors in high
tilted magnetic fields [see A.G. Lebed, Phys. Rev. Lett. $\textbf{115}$, 157001
(2015).] All calculations in the Letter, were done by using the quasi-classical
Peierls substitution method, whose applicability in high magnetic fields was
questionable. Here, we solve a fully quantum mechanical problem and show that
the main qualitative conclusions of the above mentioned Letter are correct. In
particular, we show that in high magnetic fields, applied along one of the two
main crystallographic axis, we have 2D electron spectrum, whereas, for
directions of high magnetic fields far from the axes, we have 1D electron
spectrum. The later is known to promote non-Fermi-liquid properties. As a
result, we expect the existence of Fermi-liquid - non-Fermi-liquid angular
crossovers or phase transitions. Electronic parameters of Q1D conductor
(Per)$_2$Pt(mnt)$_2$ show that such transitions can appear in feasible high
magnetic fields of the order of $H \simeq 20-25 \ T$.
