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This is a two-dimensional model of the simplest molecular ion, consisting of two protons and one electron. The electron, represented by a red-yellow probability wave, interacts with each proton, shown as blue dots, through a nonsingular Coulomb potential, defined as V(r) = -1/(r + ε). The system is confined within a box with perfectly reflecting walls (grey square). The cyan curve represents the mean position of the electron. The time evolution of the electron's probability density has been computed by numerically solving the time-dependent Schrödinger equation.

Calculate the following integral: Solution:

Calculate the following limit. Here is the solution.