  A systematic study of the energetics of electrons in an interface in a
magnetic field is reported with exact analytical calculations based on a Landau
Level (LL) picture, by serious consideration of the finite thickness of the
Quantum Well (QW). The approach is physically transparent and subtly different
in its line of reasoning from standard methods avoiding any semi-classical
approximation. We find "internal" phase transitions (at partial LL filling) for
magnetisation and susceptibility that are not captured by other approaches and
that give rise to nontrivial violations of the standard de Haas-van Alphen
periods, in a manner that reproduces the exact quantal astrophysical behaviours
in the limit of full three-dimensional (3D) space. Upon inclusion of Zeeman
splitting, additional features are also found, such as global energy minima
originating from the interplay of QW, Zeeman and LL Physics, while a
corresponding calculation in a Composite Fermion picture with {\Lambda}-Levels,
leads to new predictions on magnetic properties of an interacting electron
liquid. By pursuing the same line of reasoning for a topologically nontrivial
system with a relativistic spectrum, we find evidence that similar effects
might be operative in the dimensionality crossover of 3D strong topological
insulators to 2D topological insulator quantum wells.
