We have solved the two-dimensional time-dependent Schödinger equation for a particle with and without the interparticle potential in a fusion plasma. It was shown that spatial extent of a free particle grows monotonically in time. Such expansion leads to a spatial extent or size of a proton of the order of the average interparticle separation Δl ≡ n−1/3 ∼ 2 × 10−7 m in a time interval of 106 × Δl/vth ∼ 10−7 sec for a plasma with a density n ∼ 1020 m−3 and a temperature T = mvth2/2 ∼ 10 keV. It was also shown that, under a Coulomb potential, the wavefunction of a charged particle first shrink and expand in time. In the expansion phase, at times t ≥ 10−10 sec, the size of particle in the presence of a Coulomb potential is much larger than that in the absence of it.
