Correspondence principle in arbitrary coordinates

QuantumCosmo
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Hi,
I am currently learning for a test in theoretical physics and in one of my books it was mentioned that there is a reason why the correspondence principle only works in cartesian coordinates. Sadly, they didn't give that reason nor a book or website where one could look it up if interested.
Does anyone here know why it only works in cartesian coordinates?
Thanks in advance,
QuantumCosmo
 
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Not really. The correspondence principle says that (Wikipedia) "the behavior of a quantum system reproduces that of a classical system in the limit of large quantum numbers". All I can think of is that in non-Cartesian coordinates the correspondence does not always hold going the other way, and low quantum numbers are sometimes necessary too. For example a classical system that was axially symmetric would have m = 0.
 
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