The discussion revolves around the most likely position of an electron in a hydrogen atom, particularly in the context of its radial probability density and the implications of using Cartesian coordinates versus spherical coordinates. Participants explore the nuances of probability density, expectation values, and the interpretation of quantum states.
Participants express multiple competing views regarding the interpretation of probability density and the electron's most likely position. There is no consensus on whether the electron is more likely to be found near the nucleus or at the Bohr radius.
Limitations include unresolved mathematical interpretations, the dependence on coordinate systems, and the complexities of quantum mechanics that affect the discussion of probability and position.
Sigh. Of course you can, in principle, ask about the position of an electron in the 1S state of a hydrogen atom. Nothing forbids to measure observables of a system only because the system is not in an eigenstate of the measured observable. It's only that due to the preparation in this state the position is indetermined, and you'll find a probability density when repeating the same measurement on many electrons prepared in this 1S state.Vanadium 50 said:My point is that they don't commute with the variables you have already specified. Maybe that was unclear.
And while you can calculate what the probability was, you cant calculate what it is. "The electron is in a 1S state" and "the electron is over here" (or even "not over here") are incompatible.