On the minimum set of physical assumptions leading to the Schrödinger equation
The way of obtaining the Schrödinger equation for a quantum particle in an electromagnetic field is revisited, showing that very few physical assumptions are required. In fact, after having introduced the general formalism of non-relativistic quantum mechanics, it is shown that the structure of the Schrödinger equation for a spinless particle is obtained merely by requiring continuity of space and time, and covariance with respect to Galilean transformations. Both the Correspondence and Uncertainty principles then become «theorems».
PACS 03.65.BzFoundations, theory of measurement, miscellaneous theories (including Aharonov-Bohm effect, Bell, inequalities, Berry's phase)
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