Homework Statement
An atomic system has 2 alternative 2-state bases. The angular momentum bases are \left | \mu_i \right \rangle with L_0 = 0 and L_1 = 1. The energy eigenstates are \left | \phi_i \right \rangle with E_0 and E_1.
All states are normalised and:
\left | \mu_0 \right...
Homework Statement
The questions asks for a proof that if a geometrical transformation R on a three dimensional vector space with metric \eta is length preserving, then R^{T}\eta R=\eta. Note that the summation convention is used throughout.
The transformation is given by
x'_{i}=R_{ij}x_{j}...