Combining Relativity and Quantum Mechanics – A first step

Quantum Mechanics starting point – The Schrodinger Equation

(1)   \begin{equation*}    i\hbar\frac{\partial\psi}{\partial t} = H \psi \end{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

(2)   \begin{equation*} H = \sqrt{p^2 + m^2 c^4} \end{equation*}

If we substitute this into the above equation, we get:

(3)   \begin{equation*}    i\hbar\frac{\partial\psi}{\partial t} =  \sqrt{p^2 + m^2 c^4} \psi \end{equation*}

We need to promote the momentum in the above equation to an operator – which is done by substituting  i\hbar \frac{\partial}{\partial x} for p

(4)   \begin{equation*}    i\hbar\frac{\partial\psi}{\partial t} =  \sqrt{\hbar^2 \nabla^2 + m^2 c^4} \psi \end{equation*}

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.

Specializing in high volume web and cloud application architecture, Anuj Varma’s customer base includes Fortune 100 companies (, British Petroleum, Schlumberger).
Anuj’s training as a mathematical physicist followed by years of advanced computer programming is unique in the industry.

For Anuj’s popular technology seminars and science and scientific computing seminars, please visit ANUJ.COM

For Anuj’s Mathematical Models and Math Modeling related consulting , please visit

All content on this site is original and owned by AdverSite Web Holdings, Inc. – the parent company of No part of it may be reproduced without EXPLICIT consent from the owner of the content.

Anuj Varma – who has written posts on Anuj Varma, Technology Architect.

Leave a Reply

Your email address will not be published. Required fields are marked *