Advanced Quantum Mechanics Schwabl · Problem 6.3

The Coulomb Potential

Physics — Quantum Mechanics · lorentz-transformations-rotations

Problem

Show that the

N

-fold application of the infinitesimal rotation in Minkowski space (Eq. (6.2.22))

\Lambda = 1 + \frac{\vartheta}{N} \begin{pmatrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{pmatrix}

leads, in the limit

N \to \infty

, to a rotation about the

z

axis through an angle

\vartheta

(the last step in (6.2.22)).