A paradigm shift for me occurred when, I now realize, that position and momentum are random variables in QM. As such, it does not make any sense to say things like "take the derivative of the position with respect time".(adsbygoogle = window.adsbygoogle || []).push({});

Instead QM has the position and momentum operators which operate on the probability distribution. The probability distributions are inherently multi-modal (except for the ground state?). In the classical limit, the number of modes becomes infinitely dense and they approach the well know classical curves.

Here is a picture of the probability distribution for the 100th state of the quantum harmonic oscillator. The thick line is the probability distribution for the classical harmonic oscillator.

The light bulbs are beginning to turn on and I think I am ready to read a text book on Quantum Mechanics. I have heard about the one by Ballentine and I think I will start there.

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# I Position and Momentum are random variables in QM?

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