- #1

TheFerruccio

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## Homework Statement

The following is an excerpt of the derivation of the Schrodinger equation. After deriving the Klein-Gordon equation, the relativistic total energy is approximated to arrive at the Schrodinger equation.

## Homework Equations

[itex]E = mc^2\sqrt{1+\frac{p^2}{m^2c^2}}[/itex]

[itex]\approx mc^2\left(1+\frac{1}{2}\frac{p^2}{m^2c^2}\right)[/itex]

## The Attempt at a Solution

Well, frankly, I do not see how they went from the first step to the second step. Where did the 1/2 come from? How does the removal of the square root effectively approximate this? I am not seeing it. Was a conjugate used and multiplied somehow?