Abstract
Ordinary Hilbert-space quantum mechanics leads to a wrong prediction for the ground state of chiral molecules such as alanine. This does not mean that quantum mechanics is incorrect but only that it is not applied properly. A detailed analysis shows that chirality corresponds to a classical observable (a superselection rule) which is generated by the environment, i.e. by the influence of an infinite system. For both, classical observables and infinite systems, Hilbert space quantum mechanics is inappropriate and has to be replaced by algebraic quantum mechanics.
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