Quantum Mechanics starting point – The Schrodinger Equation
All laws of physics are required to be Lorentz Invariant . The above equation is not. To try and make it Lorentz invariant, we start with looking at the total energy of a relativistic particle.
Relativity starting point – The Total Energy of a Relativistic Particle
If we substitute this into the above equation, we get:
We need to promote the momentum in the above equation to an operator – which is done by substituting for p
This is the Klein Gordon equation. This equation is Lorentz Invariant – so that serves as a good check for our first step towards combining Quantum Mechanics with Relativity.