By Erhard Scheibe
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Extra info for The logical analysis of quantum mechanics
Qi (0) . . Qj (0) . . ) evolves to ( . . Qi (t) . . Qj (t) . . ) then ( . . Qj (0) . . Qi (0) . . ) evolves to ( . . Qj (t) . . Qi (t) . . ). 41) In other words, it is unnecessary to specify the labelling of the particles. That seems very appropriate as the labelling is unphysical. 41 follows from the symmetry of the velocity vector field, v i ( . . qi . . qj . . ) = v j ( . . qj . . qi . . 42) v k ( . . qi . . qj . . ) = v k ( . . qi . . qj . . 40. 41, let us consider a system of N identical particles.
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In the usual approach the quantization of the spectrum arises from the basic condition that in the case in which limq→±∞ W > 0, the wavefunction should vanish at infinity. Once 32 Quantum Trajectories the possible solutions are selected, one also imposes the continuity conditions whose role in determining the possible spectrum is particularly transparent in the case of discontinuous potentials. For example, in the case of the potential well, besides the restriction on the spectrum due to the L2 (R) condition for the wavefunction (a consequence of the probabilistic interpretation of the wavefunction), the spectrum is further restricted by the smoothly joining conditions.
The logical analysis of quantum mechanics by Erhard Scheibe