Since the Schr�dinger equation is only valid for non-relativistic quantum mechanics, the solutions it yields for the hydrogen atom are not entirely correct.
22.
In non-relativistic quantum mechanics, the square-modulus of the wavefunction gives the probability density function " ? " 2 } }.
23.
Similarly, in non-relativistic quantum mechanics the spin of a particle is a constant vector, but in relativistic quantum mechanics spin depends on relative motion.
24.
Similarly, in non-relativistic quantum mechanics the spin of a particle is a constant vector, but in relativistic quantum mechanics spin depends on relative motion.
25.
In dimension 3, defining the gamma matrices to be the Pauli sigma matrices gives rise to the familiar two component spinors used in non relativistic quantum mechanics.
26.
In relativistic quantum mechanics, Schr�dinger's equation becomes a wave equation as was usual in classical physics, except that complex-valued waves are considered.
27.
In non-relativistic quantum mechanics, Schr�dinger's equation for a time-varying wave function in one-dimension, not subject to external forces, is
28.
In non-relativistic quantum mechanics, this current is always well defined because the expressions for density and current are positive definite and can admit a probability interpretation.
29.
On the other hand, the existence of antiparticles leads to the conclusion that relativistic quantum mechanics is not enough for a more accurate and complete theory of particle interactions.
30.
For the case of the absence of matter, quantum field theory is necessary, because non-relativistic quantum mechanics with fixed particle numbers does not provide a sufficient account.
