In Hegerfeldt, 1998 paper "Instantaneous Spreading and Einstein Causality in Quantum Theory" he states that,
"In nonrelativistic quantum mechanics the immediate spreading of wave functions over all space is a well known phenomenon".
In which he states that it is of no concern. What does he mean by the spreading of the wave function? and if so isn't this a causality violation in the non-relativistic QM.
In non relativistic QM the solutions of the (free) Schroedinger equation have the same properties as the solutions of the heat equation: suppose that at time $t=0$ the solution (wavefuncion) $\psi(t=0, \vec{x})$ vanishes outside a spatial bounded region. For every arbitrarily large $R>0$ and every arbitrarily small time $t>0$, there are points $\vec{x}$ with $||\vec{x}|| >R$ such that $\psi(t,\vec{x}) \neq 0$.
In principle this is not a problem since, in non-relativistic physics, there is no finite bound for propagation velocities.
