The discussion centers on the radial probability density of an electron in the 1s state of a hydrogen atom, specifically its peak at the Bohr radius (a0). Participants clarify that while the probability density function (|ψ|2) peaks at the nucleus, the actual likelihood of finding the electron near the nucleus is lower due to the volume element in spherical coordinates. The conversation emphasizes that "most probable" does not equate to "probable," and the electron's position cannot be accurately described in Cartesian coordinates due to the non-commuting nature of quantum mechanical variables.
PREREQUISITESThis discussion is beneficial for physics students, quantum mechanics researchers, and educators seeking a deeper understanding of electron probability distributions and the implications of quantum theory on particle localization.
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.