Quantum-mechanical conjugate of the hamiltonian operator
196938 pages
Published in:
- Nuovo Cim.B 63 (1969) 271-308
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Abstract: (Springer)
Conjugate functions of various classical Hamiltonians are studied and different methods for their construction are presented. From these classical functions, for many dynamical systems, Hermitian operators can be found which depend linearly on time and are conjugates of Hamiltonian operators. The eigenvalues of conjugate operators, under certain conditions, represent the result of measurement of time in nonrelativistic quantum mechanics. Because of this property « time operators » may be used to study the quantum theory of microscopic clocks and to determine their accuracy. For noninteracting relativistic particles with spin zero and spin one-half a direct method of obtaining time operator is given. These conjugate operators have been used to derive well-known relations of the time delay and the rate of change of phase shift with energy in scattering theory.- quantum mechanics
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