Analytic wave functions of quasistable quantum systems with arbitrary angular momentum
W. van Dijk
Abstract We derive the exact wave function for the decaying quasistable quantum system with arbitrary orbital angular momentum. We show that this wave function can be expressed as an expansion in terms of Moshinsky functions, thereby generalizing the result for the known S -wave case to all partial waves. As a simple illustrative example, we consider a δ -shell potential, which allows us to describe the time evolution of the wave function and the associated non-decay probabilities in a transparent manner. At long times, the nondecay probability exhibits a power-law dependence on the orbital angular momentum, decreasing as t −(2 ℓ +3) , where ℓ denotes the orbital angular momentum quantum number.
Physica Scripta•Apr 20, 2026•0 citations