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.