I infer from you terse reply that the decay is seen in the imaginary part of the eigen-value. It becomes an exponential decay of the state amplitudes. Yes?Hermitian operators always have real eigenvalues. Non-Hermitian operators can have complex eigenvalues. The evolution of an eigenstate of the Hamiltonian is ~exp(-iEt) where E is the energy. If E is complex, there could be a decay.
Yes, imaginary eigenvalues mean that the probability of finding the particle decreases exponentially with time (decay). However, you should keep in mind that this is an approximate way to study decays. In this approach the probability is not conserved and the evolution is non-unitary, which contradicts basic postulates of quantum mechanics.I infer from you terse reply that the decay is seen in the imaginary part of the eigen-value. It becomes an exponential decay of the state amplitudes. Yes?
very cool. ThanksYes, imaginary eigenvalues mean that the probability of finding the particle decreases exponentially with time (decay). However, you should keep in mind that this is an approximate way to study decays. In this approach the probability is not conserved and the evolution is non-unitary, which contradicts basic postulates of quantum mechanics.
If you want to have a rigorous model of decays, you'll need to form a bigger Hilbert space, which includes states of both unstable particle and its decay products. In this Hilbert space the decay can be described by a Hermitian Hamiltonian and unitary time evolution operator. The total probability will be conserved, as required. The decreasing probability of finding the particle will be compensated by increasing probability of finding decay products.