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A simple definition to Non-Relativistic Quantum mechanics?

  1. Nov 2, 2012 #1
    What is it in a simple definition, and how does it differ from relativistic quantum mechanics?
     
  2. jcsd
  3. Nov 2, 2012 #2

    jtbell

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    Staff: Mentor

    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.
     
  4. Nov 2, 2012 #3
    but what are non-relativistic equations?
    and why does energy and momentum stand out in this definition? why not other physical quantities?
     
  5. Nov 2, 2012 #4

    jtbell

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    Staff: Mentor

    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.
     
  6. Nov 3, 2012 #5
    oh thank you loads :)!
     
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