Abstract: In quantum mechanics, unbounded operators correspond to observables like position and momentum. These operators do not have eigenvectors for single value in standard Hilbert space. Fine (1971) and Teller (1979) brought this weird fact to the attention of philosophers. In the following we investigate the different proposed solutions of the problem. In section 2. we follow Weyl’s method of exponentiation of CCR; in part 3. we examine briefly rigged Hilbert space approach; in section 4. we discuss two papers by Halvorson, which face the question from many points of view and propose two different solutions; in section 5. we reject Teller’s too metaphysical proposal; some concluding remarks follow.
Operatori a spettro continuo. Una questione zenoniana
vincenzo fano;roberto macrelli
2021
Abstract
Abstract: In quantum mechanics, unbounded operators correspond to observables like position and momentum. These operators do not have eigenvectors for single value in standard Hilbert space. Fine (1971) and Teller (1979) brought this weird fact to the attention of philosophers. In the following we investigate the different proposed solutions of the problem. In section 2. we follow Weyl’s method of exponentiation of CCR; in part 3. we examine briefly rigged Hilbert space approach; in section 4. we discuss two papers by Halvorson, which face the question from many points of view and propose two different solutions; in section 5. we reject Teller’s too metaphysical proposal; some concluding remarks follow.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
