Common Sense¶

Units¶

Natural units makes the calculation of neutrinos convinient. The consequences are

The energy-mass-momentum relations becomes $E^2 = p^2 + m^2$ . Thus mass $m$ , momentum $\mathbf p$ and energy $E$ have the same units.
Angular momentum in quantum mechanics is $L_z = m\hbar$ where $m$ is a number. $\hbar$ is of unit angular momentum.
A plane wave in quantum mechanics is $\Psi = A e^{ \frac{E t - p x}{\hbar} }$ . $\frac{E t - p x}{\hbar}$ should be unitless, which means $px$ has unit angular momentum, which is obvious, while $E t$ also has the unit of angular momentum. Previously we noticed momentum has the same unit with energy, we should have time $t$ has the same unit as length $x$ . Also we can conclude that length and time has the unit of $1/E$ .