Piotr Garbaczewski and Witold Karwowski
Impenetrable Barriers and Canonical Quantization
(64K, Revtex4, Latex)

ABSTRACT.  We address an apparent conflict between the traditional 
canonical quantization framework of quantum theory and spatially 
restricted quantum dynamics when the translation invariance of 
an otherwise free quantum system is broken by boundary 
conditions. By considering the example of a particle in an 
infinite well, we analyze spectral problems for related confined 
and global observables. In particular, we show how we can interpret 
various operators related to trapped particles by not ignoring the rest 
of the real line that is never occupied by a particle.