5 1 4 D O C . 5 1 6 S C H R Ö D I N G E R ’ S W A V E M E C H A N I C S Each corresponds, according to (1), to a summand of the system’s kinetic energy, which we assign to the pertinent principal direction. In the local system, ac- cording to (2), . … (2a) According to (1) and (3b), furthermore, . … (6) Now we introduce the hypothesis that the velocity components in the principal di- rections correspond to their due proportions of the kinetic energy. Therefore, we set accordingly . … (7) Thus the velocity components of the system (except for the sign) are determined by the wave function ψ, and there only remains the task of transferring this result to the original coordinate system. Through application of (5) to the local system and to the fundamental direction, assigned to index α, one obtains . But since is equal to 1 for , but otherwise vanishes, it follows from this or . … (8) On the other hand, the ’s are the components of the unit vector in the principal direction α. Hence, is that portion of the μ-component of the velocity that emerges from the velocity of the system in the principal direction α. Through sum- mation over all the principal directions, we obtain … (9) From (9), taking (7) and (8) into account, one gets ψαα 2L 2· α ¦qα = 2L h2-ψαα 4π2 ψ - –-----------------· ¹ § α ¦© = qα 2· h2-ψαα 4π2 ----------------- ψ - –= ψμν λ(α)δμν)A(να) – ( 0= A(να) ν α = ψαβ λ( α) δαβ = ψαα λ( α) = ψαβ 0 = (if α β) ≠ ( A(μα) qαA(μα) · qμ · · α ¦qα A(μα) =