Wave Mechanics 203
calculation of the lifetime of unstable nuclei based on barrier penetration
has given excellent agreement with experimental value confirming the
quantum mechanical effect of tunneling. This effect is strictly quantum
mechanical and would not be possible were it not for the uncertainty
principle. When the particle passes through the forbidden zone, a
violation of energy conservation takes place. The time during which this
violation occurs, ∆t, is very small so that the product of the energy
conservation discrepancy times the time the particle is in this state is
less than h. But according to the uncertainty principle the product of
the uncertainties ∆E times ∆t is greater than h, hence the energy
conservation violation can never be detected because measurements
accurate enough to show this are not possible. This is one of the
mysteries of quantum mechanics.