The $N$-dimensional Schrödinger equation involving a general, central potential $V_N(r)$, is decomposed into a 3-dimensional component plus a term that may be treated as a dimension-dependent perturbation. This allows discussion of the general $N$-dimensional system from a 3-dimensional perspective.
MAVROMATIS, Harry A. (1998) "Dimensionality and Energy Levels of Quantum Mechanical Systems," Turkish Journal of Physics: Vol. 22: No. 2, Article 3. Available at: https://journals.tubitak.gov.tr/physics/vol22/iss2/3