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bhobba said:Exactly where does Ballentine say it? He examines the issue of probability in QM on page 55 if you want to look it up.

I don't have Ballentine, but what I learned was the same as in Wikipedia:

https://en.wikipedia.org/wiki/Wave_function#cite_note-8The unit of measurement forψdepends on the system, and can be found by dimensional analysis of the normalization condition for the system. For one particle in three dimensions, its units are [length]−3/2, because an integral of |ψ|2 over a region of three-dimensional space is a dimensionless probability.https://en.wikipedia.org/wiki/Wave_function#cite_note-8

https://en.wikipedia.org/wiki/Wave_function