Sunday, November 23, 2014

Something Old, Something New, A Shoulder To Rely On

From the post "We Have A Problem, Coulomb's Law",

\(F=2\cfrac { mc^{ 2 } }{ x } e^{i\pi/2}\)

So,

\(\psi=-\int{2\cfrac { mc^{ 2 } }{ x } e^{i\pi/2}}d\,x\)

\(\psi=-{2{ mc^{ 2 } }{ ln(x) } e^{i\pi/2}}\)


Similarly \(\psi\) is delimited at \(x=x_a\), where \(\psi=0\).  However, without \(A\) (cf. post "Not Exponential, But Hyperbolic And Positive Gravity!"), Coulomb's Law applies for all \(x\gt0\).

\(F=\cfrac { mc^{ 2 } }{ 6\pi x^2 } e^{i\pi/2}\)

Nice to know there's something old to fall back on.