(adsbygoogle = window.adsbygoogle || []).push({}); Mentor note: fixed formulas so they get displayed properly

If we take the K-G eqn and the following term for the wave function

$$( \partial^2 + \frac{m^{2}c^{2}}{\hbar^{2}})\Psi =0

\\\\\Psi = Re^{-i\omega t + i k_{i}x_{i}}$$

We worked through to this ##\hbar \omega = \pm \sqrt{\hbar^{2} c^{2}k_{i}k_{i}+ m^{2}c^{4}}## which is fine and recognisable, but I cant get the ##\hbar^{2} c^{2}k_{i}k_{i}## term to equal the familiar ##\rho^{2}c^{2}##. I'm assuming it's obvious and thats why he didnt show it, but I'm a bit stuck.

Any help would be appreciated.

edit

he also did something similar here:

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# Stuck on last part of class derivation (proof) K-G Eqn

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