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Originally Posted by GUILLE What is dirac's linear equation and why/how is it solved? |
The relativistic form of Schroedinger's original wave equation is quadratic in the partial derivative with respect to time. It was able to demonstrate agreements with the Balmer formula of spectral analyses. However, it failed to account for the correct fine structure of the hydrogen D-doublet spectral lines. At this time, many people were working on this problem. They were working on a scalar wave equation which could basically give a nonpositive definite probability density since squares of all negative and positive densities give positive answers. Dirac believed at the time that the requirement for positive definite probability densities must have their wave equation linear in the partial time derivative.