I followed -Concepts of Modern Physics --by Arthur Beiser --- and in the Derivation of Schrödinger Equation, The author says---> (chapter 5.3)--> At speeds small compared to the speed of light, the Total Energy of a Particle is sum of its Kinetic Energy K.E. and Potential Energy U, And Shows that(adsbygoogle = window.adsbygoogle || []).push({});

Total Energy E = p^{2}/2m + U

But according to the Theory of Relativity, The total Energy of a particle is sum of its kinetic Energy and Rest mass Energy + (potential Energy, if present)

So the Relation had to be (for what I think) --->

Total Energy E = p^{2}/2m + U + m_{0}c^{2}.

Why is the Author not considering the rest Energy???

The derivation in the book, is almost same as here --

http://hyperphysics.phy-astr.gsu.edu/hbase/HFrame.html

Oops, just noticed that the link don't directly take you there. For now, First Click Quantum Mechanics, then Schrödinger's Equation

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# Derivation of Schrodingers Equation

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