How Does the Schrödinger Equation Account for Rest Mass Energy?

[hyena]

i know its a stupid question but I am a beginner:
according to eisntein:
$$E=K+m_{o}c^2$$
but the plane wave solution yields that particle's KE is its total energy,where free particle has no potential energy. But where is the rest mass energy$$m_{o}c^2$$? Is it omitted?

 

[jtbell]

Schrödinger's equation is non-relativistic.

 

[Avodyne]

If we start with

$$E=\sqrt{p^2 c^2 + m^2 c^4}$$

and Taylor-expand in powers of $p$, we get

$$E=mc^2 + {p^2\over 2m} + \ldots$$

The second term is the usual nonrelativistic kinetic energy. The first term is a constant, and so could be added to the potential energy. But it has no physical consequences, so it's just omitted for convenience.