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A unified approach to the time analysis of tunnelling of nonrelativistic particles is presented, in which Time is regarded as a quantum-mechanical observable, canonically conjugated to Energy. The validity of the Hartman effect (independence of the Tunnelling Time of the opaque barrier width, with Superluminal group velocities as a consequence) is verified for all the known expressions of the mean tunnelling time. Moreover, the analogy between particle and photon tunnelling is suitably exploited. On the basis of such an analogy, an explanation of some recent microwave and optics experimental results on tunnelling times is proposed. Attention is devoted to some aspects of the causality problem for particle and photon tunnelling. †

-We study the phenomenon of one-dimensional non-resonant tunneling through two successive (opaque) potential barriers, separated by an intermediate free region R, by analyzing the relevant solutions to the Schroedinger equation. We find that the total traversal time does not depend not only on the barrier widths (the so-called "Hartman effect"), but also on the R width: so that the effective velocity in the region R, between the two barriers, can be regarded as practically infinite. This agrees with the results known from the corresponding waveguide experiments, which simulated the tunneling experiment herein considered due to the known formal identity between the Schroedinger and the Helmholtz equation.

Some results are reviewed and developments are presented on the study of Time in quantum mechanics as an observable, canonically conjugate to energy. Operators for the observable Time are investigated in particle and photon quantum theory. In particular, this paper deals with the hermitian (more precisely, maximal hermitian, but non-selfadjoint) operator for Time which appears: (i) for particles, in ordinary non-relativistic quantum mechanics; and (ii) for photons (i.e., in first-quantization quantum electrodynamics).

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We obtained the spectrum of probability of the bremsstrahlung emission accompanying the α-decay of 226 Ra (Eα=4.8 MeV) by measuring the α-γ coincidences and using the model presented in our previous study on the α−decay of 214 Po (Eα=7.7 MeV). We compare the experimental data with the quantum mechanical calculation and find a good agreement between theory and experiment. We discuss the differences between the photon spectra connected with the α-decay of the 226 Ra and 214 Po nuclei. For the two mentioned nuclei we analyze the bremsstrahlung emission contributions from the tunneling and external regions of the nucleus barrier into the total spectrum, and we find the destructive interference between these contributions. We also find that the emission of photons during tunneling of the α-particle gives an important contribution to the bremsstrahlung spectrum in the whole Eγ energy range of the studied 226 Ra nucleus.

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