PNMS Mode B — Quantum Mechanics Branch: Φ_R Coupled to the Schrödinger Equation

Branch document connecting the PNMS constructive operation (Mode B) to quantum mechanics. The document defines how the PNMS projection operator Φ_R is applied to systems described by the Schrödinger equation. It specifies the active quantities used in the analysis — binding energy, orbital radius, particle mass, orbital period, and state degeneracy — and identifies the corresponding rows in the PNMS reference basis. The document establishes the constraint relation (|E| / E_p) · (a / l_p) = 3.6471 × 10⁻³ which defines the quantum-mechanical constraint surface for hydrogen bound states in PNMS signature space. It also defines the constructive operation used to generate and verify quantum states and introduces the quantum-mechanics case study series associated with this branch.