The dynamic foundation of quantum mechanics

Quantum mechanics has been reinvented via mathematical incarnation of Newton's 2$^{nd}$ law in word for particle motion with an \textit{almost} \textit{nowhere} differentiable path. At \textit{almost every} radius vector$x$, the particle has a velocity \textbf{\textit{u}} in time forward and $\widetilde{u}$ in reversal. We formulate that$u=u_n +u_b $. The assumed stochastic radiation in vacuum causes that$\delta x_i \delta x_j =\delta _{ij} 2D\delta t\equiv \delta _{ij} \left( {\hbar \mathord{\left/ {\vphantom {\hbar m}} \right. \kern-\nulldelimiterspace} m} \right)\delta t$. That$\left[ {\left( {\partial \mathord{\left/ {\vphantom {\partial {\partial t}}} \right. \kern-\nulldelimiterspace} {\partial t}} \right)+u_n \cdot \nabla -iu_b \cdot \nabla -i\left( {\hbar \mathord{\left/ {\vphantom {\hbar {2m}}} \right. \kern-\nulldelimiterspace} {2m}} \right)\nabla ^2} \right]\left( {p_n -ip_b } \right)=K_n -iK_o $ emerges as the 2$^{nd}$ law; where $K_n $is an even function of time and $K_o $odd. Employing this law, we derive the Schr\"{o}dinger equation with the paradigm,$\left( {-i\hbar \nabla -qA} \right)\psi =\left( {p_n -ip_b } \right)\psi $, in pediatrician terms. Those $\nabla ^2\rho \left( {x_j } \right)=0$ specify$x_j \mbox{'s}$, where$p_b \mbox{'s}$are \textit{exactly} defined. For the case$A\equiv 0$, there are two pure cases: (a) $p_b $only; (b) $p_n $only. Miscategorization of$p_b $as$p_n $in quantum theory \textit{status quo} is revealed in (a). Energy is \textit{numerically} \textit{computed} at$x_j \mbox{'s}$, which explain atomic stability. That$p_n \cdot d=nh$ is the law of transmission of $p_n $ through crystal planes, is derived in (b). Summary also on web: http://mysite.verizon.net/vjtlee/