Energy additional formula : I don't know exactly what you're seeking for, but an easy method is : from the most general type of equation we seek : [math]E^n=c^\alpha p^\beta m^\gamma[/math] in units we get : [math]\frac{m^{\alpha+\beta}kg^{\beta+\gamma}}{s^{\alpha+\beta}}=\frac{m^{2n}kg^n}{s^{2n}}[/math] for [math]n=1[/math], we can with this "strange/silly", or what we call "turning in round methods/mathematics" get the following relations, with for example : the triples {[math]\alpha,\beta,\gamma[/math]}={1,1,0},{0,2,-1},{-1,3,-2},{-2,4,-3},... and hence a possible equation with coefficient [math]A_i[/math] [math]E=A_1pc+A_2\frac{p^2}{m}+A_3\frac{cp^3}{m^2}+...[/math] and if we canonically quantize, [math]E\rightarrow i\hbar\partial_t, p\rightarrow -i\hbar\partial_x[/math] : [math]-i\hbar\frac{\partial\Psi}{\partial t}=A_1\frac{-i\hbar\partial\Psi}{\partial x}+A_2\frac{-\hbar^2\partial^2\Psi}{\partial x^2}+A_3\frac{-ic\hbar^3\partial^3\Psi}{m^2\partial x^3}+...[/math] if but you seek variation on c, you get : [math]E=pc+c^2m+c^3m^2/p+c^4m^3/p^2+c^5m^4/p^3+c^6m^5/p^4+c^7m^6/p^5+...[/math] "The method of people that know nothing to do"