ABSTRACT
The importance of Ehrenfest’s “Adiabatic Hypothesis” for the present and future of the quantum theory makes very desirable an exact examination of its purely mechanical meaning. Some years ago one of the authors1 found a general method to look for the adiabatic invariants, whereas the other author2 investigated the case of a degenerated, conditionally periodic system which had not been considered in the first paper (see also the paper by Burgers3). An objection which can be attributed to this theory is that in the course of calculations at some point a simplifying assumption was made in the integrated differential equations, namely that its right-hand side is subject to an averaging process; to explain this approximation, arguments connected with the slowness of changes of the system parameters were used. This shortcoming makes it difficult to use the ordinary methods and to check the adiabatic invariance of several quantities. Therefore it seems reasonable to consider a very simple example which we can integrate without any additional assumptions and only then use the slowness of parameter changes.
