>An unstable particle capable of undergoing real decay - N + theta is considered in the nonrelativistic second quantization theory (Lee model). Perturbation theory and the expansion of an arbitrary state in eigen states are extended to the case of an unstable particle. The quantity which plays the role of the state norm of such a particle is determined. A new method is proposed for determining the fraction of time a stable particle V capable of undergoing the virtual transformation into N + theta stays in the state V and in the state N + theta . If the method is applied to an unstable particle V, one can find the time it is in each of the two states, but the answer is expressed in complex numbers. (auth)
We consider a model of a unstable state defined by the truncated Breit-Wigner energy density distribution function. An analytical form of the survival amplitude
a(t) of the state considered is found. Our attention is focused on the late time properties of
a(t) and on effects generated by the non--exponential behavior of this amplitude in the late time region: In 1957 Khalfin proved that this amplitude tends to zero as
t goes to the infinity more slowly than any exponential function of
t. This effect can be described using a time-dependent decay rate
γ(t) and then the Khalfin result means that this
γ(t) is not a constant but at late times it tends to zero as
t goes to the infinity. It appears that the energy
E(t) of the unstable state behaves similarly: It tends to the minimal energy
Emin of the system as
t→∞. Within the model considered we find two first leading time dependent elements of late time asymptotic expansions of
E(t) and
γ(t). We discuss also possible implications of such a late time asymptotic properties of
E(t) and
γ(t) and cases where these properties may manifest themselves.