FIG. 4: The plot of quantum probability density ρ$_{n}$ ( r ) = | ψ$_{n}$ ( x ) | 2 (solid line), where ψ$_{n}$ ( x ) is the wave function (3.12) and the classical probability density ρ$_{cl}$ ( r ) (dashed line) given by (3.13), where r$_{max}$ = r$_{max}$ ( E$_{n}$ ) = √$_{2}$$_{E}$ n κ . We set c = 1 ms − $^{1}$, κ 2 = 1 Jm − $^{2}$, and ℏ = 1 Js. Therefore, by virtue of the first equation of Eq. (2.3) we have We finally write down the following approximate relation obtained numerically: 13 〈 ψ$_{n}$ | ˆ rψ$_{n}$ 〉 ≈ r$_{max}$ ( E$_{n}$ ) 2 = √$_{2}$$_{E}$$_{n}$ 2 κ , (3.19) 〈 cp 〉 cl = 2 3 E. (3.18)