Hello /sci/,

I am studying the Klein Gordon Equation, and have a question.

https://www.youtube.com/watch?v=WqoIW85xwoU&ab_channel=DanFleisch

It seems an interesting marriage between quantum operators and special relativity. However, I have a concern I'm wondering if any anons here know where it could be addressed.

The deriviation utilizes the first two order terms for the momentum-energy equivalence
$<br /> \sqrt{\textbf{p}^2c^2 + m^2c^4} = E<br />$
under the assumption that we are at low speeds. I want to drop this assumption and see this equation done with the expanded power series
$<br /> E = m_0c^2[1 + \frac{1}{2}(\frac{v}{c})^2 + \frac{3}{8}(\frac{v}{c})^4 + \frac{5}{16}(\frac{v}{c})^6 + ...]<br />$

Does any anon have insight or material that deals with this?

Much thanks