LFM/QM-13 :: Normalization of Continuous Energy Solutions

Question : How best to normalize continuous energy solutions?

Almost no book,  discusses how continuous energy solutions for potential problems are normalized? It is understood that one can use \[\int_{-\infty}^\infty u_E^*(x) u_{E^{\,\prime}}(x)\, dx = \delta(E-E^{\,\prime})\]. It turns out that, apart from free particle solutions,  this normalization is  inconvenient in most cases and cumbersome to implement.
Landau Lifshitz suggest that the value of current density, at some chosen point, may be used to give unit flux. This is useful, has physical interpretation and simple to implement.

Landau L. D. and Lifshitz E. M. "Probability Current"  \(\S\) 19
"Non Relativistic Quantum Mechanics' 3rd Edn,  Pergamon Press