TITLE:
Geometric Origin of Quantization: Deriving the Schrödinger Framework from NUVO Scalar Coherence
AUTHORS:
Rickey W. Austin
KEYWORDS:
NUVO Space, Scalar Geometry, Quantization, Coherence, Scalar Field Modulation, Loop Dynamics
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.1,
December
31,
2025
ABSTRACT: We prove that the stationary NUVO scalar transport equation
λ
2
∇
η
2
ψ+(
2
∇
η
lnλ⋅
∇
η
+
∇
η
2
lnλ
)ψ=0
is gauge-equivalent, under
ψ=ϕ/λ
, to a Schrödinger eigenproblem
(
−
ℏ
2
2m
Δ+
V
phys
+
V
eff
[ λ ]
)ϕ=Eϕ
, with geometric potential
V
eff
[ λ ]=
ℏ
2
2m
(
|
∇lnλ |
2
−Δlnλ
)
. Under mild decay bounds on
∇lnλ
and
Δlnλ
,
H
λ
is semibounded and self-adjoint via the Friedrichs extension; for Kato-class
V
phys
the operator domain equals
H
2
(
ℝ
3
)
. If additionally
λ,
λ
−1
∈
L
∞
, the map
ϕ↦ϕ/λ
is a bounded similarity on
L
2
. We give solvable profiles, a Birman-Schwinger/Lippmann-Schwinger representation, and a coupled partial-wave system for anisotropic
λ
. Consistency checks (constant
λ
, hydrogenic expectations) and spin terms from a conformal Dirac reduction confirm the construction. In combination with prior results of Quantization III, this paper establishes the Schrödinger framework as a scalar-geometric limit of NUVO, with
V
eff
[ λ ]
playing the role of a geometric quantum potential.