Investigation of Solutions of Quasistationary States for the Quasipotential Equation

The excited states of quantum systems are nonstationary, and they break up. These states are called unstable or quasi-stationary. Such states are already observed in the study of scattering problems, the accumulation of particles in the lens (the particle prefers to live inside the lens) is accompanied by a large delay τ (the lifetime of the quasi-level). Here the lifetime of the quasi-level τ = γ−1, width of the quasi-level Г = ~γ and complex energy level E = E1 − iE2,E2 = Γ/2. Investigation of the quasi-stationary states is carried out for the quasi-potential equation with piecewise-constant potentials at various values of the parameter of the equation ε and the potential parameters. A comparative analysis of solutions of the quasi-potential equation for the different values of ε with the solutions of the Schredinger equation is performed. Found that at ε → 0 the solutions of quasi-potential equation tend to the solutions of the Schredinger equation.

quasistationary states, the quasipotential equation, the shift operator, piecewise constant potentials