1. Hi everybody,
I am working on a model that uses the solution to a 2nd order DE, Ψ(e,ε), as probability amplitude for the electromagnetic field, EΨ(e,ε), e=elementary charge, ε=electric constant. Reversing the usual QM, this will provide particle character to a wave, giving:

- quantized values for particle energy as function of the fine-structure constant α:
W_n /W_electron = ylm1.51 Π(k=0->n) α^(-1/3^kε) n={0;1;..}, see table below for spherical sym. y00 = 1 and 1.st angular term y10 =3^1/3 =1.44.
- a numerical approximation for the fine-structure constant α^-1 ≈ 4π Γ(1/3)|Γ(-1/3)| ( Γ=Gamma function)
- magnetic moments, calculated from the electromagnetic fields; agreement with experiment within factor of 2
and on a speculative level
- a possibility to quantitatively express gravitational force entirely in electromagnetic terms,
- an indication of a common base for strong force, electromagnetism and mass/gravitation.
The model is quite incomplete, its elaboration primitive and sloppy and I know the standard model already explains everything, but I need only e + ε, the standard model needs an additional 20+ parameters to do so.

Any idea, comment or critique welcome,

Happy new year,
kwrk
.............W_lit/MeV.......Wn/We lit.......Wn/We calc.......calc/lit.......Πn/1,509
y00...(ν......0,3eV-calc.........-................... 6E-7..................-..............α^3)
.........e.......0,51...................-.......................-........................-...............-
.........µ.......105,66...........206,8........... ....206,8.............1,000.........α^(-1)
.........η.......547,86.........1072,1............ .1066,0.............0,994.........α^(-1)α^(-1/3)
.........p.......938,27.........1836,2............ .1841,5.............1,003.........α^(-1)α^(-1/3)α^(-1/9)
.........n.......939,57.........1838,7............ .1841,5.............1,002.........α^(-1)α^(-1/3)α^(-1/9)
.........Λ.......1115,68.......2183,3............. 2209,6.............1,012.........α^(-1)α^(-1/3)α^(-1/9)α^(-1/27)
.........Σ.......1192,64.......2333,9............. 2348,0.............1,006.........α^(-1)α^(-1/3)α^(-1/9)α^(-1/27)α^(-1/81)
.........Δ.......1232,00.......2411,0............. 2420,4.............1,004.........α^(-3/2)
y10. .π.........139,57..........273,1...............298,2 .............1,092.........1,44 α^(-1)
........ρ0........775,26........1517,2............1537,6.... .........1,013.........1,44 α^(-1)α^(-1/3)
........ω0........782,65.......1531,6.............1537,6.... .........1,004.........1,44 α^(-1)α^(-1/3)
........Σ0.......1383,70.......2707,8.............2656,3.... .........0,981........1,44 α^(-1)α^(-1/3)α^(-1/9)
........Ω-........1672,45.......3272,9.............3187,2... ..........0,974........1,44 α^(-1)α^(-1/3)α^(-1/9)α^(-1/27)
........tau......1776,82.......3477,.............. ..3491,3.............1,004........1,44 α^(-3/2)

2.

3. A rough sketch, details are here:
doi.org/10.5281/zenodo.801423

Ψ = exp(-(β/(2r3))

is the approximate solution of
(ħc α)2 (r 4πε/ e2) d2Ψ/dr2 - β/2 r-3 dΨ/dr + β/2 r-4 Ψ(r) = 0
Ψ will be used as kind of probability amplitude for the electromagnetic field. The integrals
∫ Ψ(r)2 r-(m+1) dr ≈ Γ(m/3, β/r3) β(-m/3) / 3 ( Γ => Gamma function) may be used for:

I point charge: Wpc = ε ∫ E2 Ψ2 d3r
II photon: Wph = hc / (∫ Ψ(r)2 dr)

The product of the integrals in I+II (energy conservation) gives:
Fine-structure constant, α-1 = 4π Γ(+1/3) |Γ(-1/3)|

Their ratio gives quantized particle energies:
Wn/Welectron = 3/2 Π(k=0-n) α^(-3/3k)

n, l.................W_calc/W_lit....α-coefficient (energy)
-1,∞....Planck......0.999.........2/3 α^(-3) (2/3α^(-3))^3 3/2 α^(-1) 2........ [source term]
0, 0.........e...........1.000.........2/3 α^(-3)
1, 0.........µ...........1.000.........α^(-3)α^(-1)
2, 0.........η...........0.993.........α^(-3)α^(-1)α^(-1/3)
3, 0.........p...........1.002.........α^(-3)α^(-1)α^(-1/3)α^(-1/9)
3, 0.........n...........1.000.........α^(-3)α^(-1)α^(-1/3)α^(-1/9)
4, 0.........Λ...........1.011.........α^(-3)α^(-1)α^(-1/3)α^(-1/9)α^(-1/27)
5, 0.........Σ............1.005.........α^(-3)α^(-1)α^(-1/3)α^(-1/9)α^(-1/27)α^(-1/81)
∞,0.........Δ............1.003.........α^(-9/2)
1, 1.........π............1.092.........α^(-3)α^(-1) 1.44
2, 1........ω0...........1.003.........α^(-3)α^(-1)α^(-1/3) 1.44
3, 1........Σ0............0.980........ α^(-3)α^(-1)α^(-1/3)α^(-1/9) 1.44
4, 1........Ω-............0.972........α^(-3)α^(-1)α^(-1/3)α^(-1/9)α^(-1/27) 1.44
5, 1........N1720.....1.005.........α^(-3)α^(-1)α^(-1/3)α^(-1/9)α^(-1/27)α^(-1/81) 1.44
∞,1........tau...........1.003........ α^(-9/2) 1.44
∞,∞.......Higgs.......1.01
9........ α^(-9/2) 3/2 α^(-1)/2

The relationship with Planck / Gravitation is no numerical coincidence. Expanding the incomplete gamma function of I gives terms for 1.) particle energy as given in table, 2.) Coulomb interaction, 3.) potential energy term of the DE, which as such is responsible for effects associated with strong interaction for r < rparticle, yet for r >> rparticle gives a quantitative term for gravitation.

Precision ~0.001, Parameter: elementary charge, electric constant;