- #1

WannabeNewton

Science Advisor

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## Main Question or Discussion Point

Heyo. On page 4 of Srednicki's QFT text, the following equation is given (in an attempt to make the Schrodinger equation relativistic): ##i\hbar \partial_t \psi(x,t) = \sqrt{-\hbar^2c^2 \nabla^2 + m^2 c^4}\psi(x,t)## where ##\psi(x,t) = \left \langle x|\psi,t \right \rangle## is the position representation of the state vector, as usual.

He then states that if we expand the square root in the RHS in powers of ##\nabla^2##, then we get an infinite number of spatial derivatives acting on ##\psi(x,t)## which implies that the above equation is non-local in space. I don't get why this implication follows (i.e. why an infinite number of spatial derivatives acting on the position-space wavefunction implies that the equation is non-local in space), could someone explain it? Thanks!

He then states that if we expand the square root in the RHS in powers of ##\nabla^2##, then we get an infinite number of spatial derivatives acting on ##\psi(x,t)## which implies that the above equation is non-local in space. I don't get why this implication follows (i.e. why an infinite number of spatial derivatives acting on the position-space wavefunction implies that the equation is non-local in space), could someone explain it? Thanks!