Quant Not Quark Ii

[kwrk]

A rough sketch, details are here:

http://doi.org/10.5281/zenodo.801423

 

Ψ( r ) = 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 = 0
Ψ will be used as kind of probability amplitude for the electromagnetic field. The integrals
∫ Ψ² r^-(m+1) dr ≈ Γ(m/3, β/r³) β^(-m/3) / 3 ( Γ => Gamma function) may be used for:

I point charge: W_pc = ε ∫ E² Ψ² d³r
II photon: W_ph = hc / (∫ Ψ² 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:
W_n/W_electron = 3/2 Π(k=0-n) α^(-1/3^k)

 

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.......1.019........ 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 <≈ r_particle, yet for r >> r_particle gives a quantitative term for gravitation.

 

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

Comments + critics welcome,
kwrk