Saturday, November 15, 2014

Wave When Small

From the post "Particle Wave Duality, Seriously MP",

\(\psi =\cfrac { mc^{ 2 } }{ 12\pi  } \cfrac { 1 }{ x^{ 3 } }\)

\(\int _{ a }^{ b\rightarrow\infty }{ \psi  }\, \partial x=\cfrac { mc^{ 2 } }{24 \pi  } \cfrac { 1 }{ a^{2} }=+finite\) --- (*)

where \(a\) is the radius of the particle.  The wave \(\psi\) was found to be of finite extend.  This is the boundary between wave and particle; beyond \(x_b\) where \(\psi\) is small as delimited by (*), the particle cease to have wave property.

\(\psi_b=\cfrac { mc^{ 2 } }{ 12\pi  } \cfrac { 1 }{ x_b^{ 3 } }\)

where \(\psi_b\rightarrow0\)

Theoretically.