D O C . 5 1 6 S C H R Ö D I N G E R S WAV E M E C H A N I C S 5 1 5 . (10) This equation, in connection with (5a), (5), and (4), solves the given task— provided the ’s are ¢everywhere² negative. There are 2n possible velocities at- tached to each spot in the configuration space. This ambiguity is to be expected a priori, in view of the quasi-periodic motions. The above consideration shows that the assignment of fully defined motions to solutions of the Schrödinger differential equation is, at least from the formal stand- point, just as possible as the assignment of definite motions to solutions of the Hamilton-Jacobi differential equation in classical mechanics. Postscript to the correction proofs. Mr. Bothe[7] has meanwhile calculated the example of an anisotropic two-dimensional resonator according to the reasoning provided here and thereby found results that, from the physical point of view, must certainly be rejected. Stimulated by this, I found out that this schema does not prop- erly take into account one general condition that must be set for a general law of motion of the systems. Specifically, a system Σ is considered, which consists of two energetically mu- tually independent partial systems and this means that the potential energy as well as the kinetic energy are composed additively of two parts, the first of which contains only quantities with reference to the second, only quantities with ref- erence to Then, as is known, , where depends only on the coordinates of depends only on the coordi- nates of In this case it must be required that the motions of the total system be combinations of possible motions of the partial systems.[8] The indicated schema does not correspond to this condition. Namely, let μ be an index that belongs to one of the coordinates of ν be an index belonging to a coordinate of Then does not vanish. This is consequently connected (comp. 5a) to that the of Σ do not agree with the of and provided each of these systems is subjected to observation as an isolated system. Mr. Grommer[9] has pointed out that this objection could be addressed by a mod- ification of the presented reasoning, in which not the scalar ψ itself is applied to the definition of the principal directions, but the scalar .[10] The implementa- tion poses no difficulty, but will be given when it has been confirmed by examples. · h 2𦱩 ------ λα ψ -----· -– ¹ § A(μα) α = λα- ψ ----- Σ1 Σ2 Σ1, Σ2. ψ ψ1 ψ2 = ψ1 Σ1 ψ2 Σ2. Σ1, Σ2. ψμν λ(α)’s λ(α)’s Σ1 Σ2, χ lgψ =
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