A simple definition to Non-Relativistic Quantum mechanics?

[M. next]

What is it in a simple definition, and how does it differ from relativistic quantum mechanics?

 

[jtbell]

In non-relativistic QM, you assume that energy and momentum are related by non-relativistic equations. In relativistic QM, you assume that energy and momentum are related by relativistic equations.

 

[M. next]

but what are non-relativistic equations?
and why does energy and momentum stand out in this definition? why not other physical quantities?

 

[jtbell]

but what are non-relativistic equations?

Consider Schrödinger's equation:

$$-\frac{\hbar^2}{2m} \nabla^2 \Psi + V \Psi = i \hbar \frac {\partial \Psi}{\partial t}$$

The terms correspond (via the QM operators for momentum and energy) to the non-relativistic

$$\frac{p^2}{2m} + V = E$$

$$K + V = E$$

i.e. kinetic energy plus potential energy equals total energy. $K = \frac{p^2}{2m}$ comes from the familiar $K = \frac{1}{2}mv^2$ for kinetic energy and $p = mv$ for momentum.

 

[M. next]

oh thank you loads :)!