Natural units

Definitions of speed of light, reduced Planck's constant, and electronvolt in terms of kilograms, meters, seconds:
 * $$ c = 299792458 \ {m\over s}$$
 * $$ \hbar = 1.054571817 \times 10^{-34} \ kg {m^2 \over s}$$
 * $$ eV = 1.602176463 \times 10^{-19} \ kg {m^2 \over s^2} $$

Then solve for second:
 * $${\hbar \over eV} = 6.582120268 \times 10^{-16} s$$
 * $$s = 1.519267287 \times 10^{15} {\hbar \over eV} $$

Solve for kilogram:
 * $$c^2 = 8.987551787 \times 10^{16}\ {m^2 \over s^2} $$
 * $${eV \over c^2} = 1.782661731 \times 10^{-36} \ kg $$
 * $$kg = 5.609589202 \times 10^{35} \ {eV \over c^2} $$

Solve for meter:
 * $$ {\hbar \over c} = 3.51767294 \times 10^{-43} \ kg \cdot m $$
 * $$ {\hbar \over c} = 1.973270014 \times 10^{-7} \ {eV \over c^2} m $$
 * $$ 5067730.179 \ {\hbar \over c} {c^2 \over eV} = m $$
 * $$ m = 5067730.179 \ {\hbar c \over eV} $$

Summarize results:
 * $$kg = 5.609589202 \times 10^{35} \ {eV \over c^2} $$
 * $$ m = 5067730.179 \ {\hbar c \over eV} $$
 * $$s = 1.519267287 \times 10^{15} {\hbar \over eV} $$
 * Dimensional conversion: $$kg^x m^y s^z \sim c^{y - 2x} \hbar^{y + z} eV^{x - y - z}$$

Now omit c and &hbar;:
 * $$kg = 5.609589202 \times 10^{35} \ eV $$
 * $$m = 5,067,730.179 \ {1\over eV} $$
 * $$s = 1.519267287 \times 10^{15} {1\over eV} $$
 * Dimensional conversion: $$ kg^x m^y s^z \sim eV^{x - y - z} $$

Based on: http://www.physics.gla.ac.uk/~dmiller/lectures/RQM_2008.pdf, page 12