1. Hamiltoniam \(H\) of the system can be expressed as sum of two Hermitian operators,
and \(H_0\) is considered as dominant term, and \(H_1\) as perturbation.
2. Initial state \(\psi\) of the system is eigenfunction of \(H_0\).
3. \(H_1\) entangles the state \(\psi\) with continuum of eigenfunctions of \(H_0\), that has continuum (or quasi continuum) set of eigenvalues.
Application of the concept of quantum decay
Quantum decay is used to describe metastable states of the system.
The metastable state is characterised in the following: Its evolution can be described with hamiltonian \(H_0\) during a time interval, large in compare to the difference between eigenvalues of the states involved.
Often the decay refers to the emission of some boson (usually a photon) by an excited (metastable) state
Examples of the quantum decay
Since century 20, the emission of light and spontaneous transformations of atomic nuclei are interpreted as quantum decay.
The famous example is discovery of the beta decay by Marie Curie.
Classical description of quantum decay
Quantum mechanics by itself is completely deterministic theory; no exponentially growing deviation in evolution of two "similar" quantum states is allowed. However, in the practical cases, at some stage of evolution of a quantum system, the result should be interpreted in terms of observable, id est, in terms of classical physics. At this moment, the description becomes incomplete, and the the probability appears in the predictions.
In the classical language, the quantum system remains in the excited state and then decays, relaxes. Often, this decay is exponential, in the sense, that probability, that the system is still excited, reduces exponentially with time. The decrement of this exponential is called decay rate.
Quantum decay is main concept in the description of the relaxation heat, that determines the explosion of the nuclear reactors at the failure of the cooling system, even if the chain reaction is shut down.
The relaxation heat provided the evaporation of the nuclear fuel to the atmosphere at the Chernobyl disaster on 1986, since the so–called "liquidators" had concentrated the radioactive debris back in the wreckage of the reactor after the explosion, converting the small accident into the global catastrophe.
The relaxation heat (id est, the qauntum decay) seems to be main reason of explosion of the reactors at the Fukushima disaster in 2011; since the shut down of the chain reaction, the vapour from the boiling water in the reactor could not be used in the main turbines, and there was no way to deliver sufficient amount of the coolant to the active zone.
Humor about quantum decay
One good guy in 1923
Made love with Marie Curie
It was nice, but next day
His dick felt out away..
Did you hear about beta-decay?