Is the opposite of quantization just taking the limit $h \rightarrow 0$ ? Or are there more steps involved (maybe related to bosons and fermions?)? How would one call the the opposite of quantization? Classization? Continuization?
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$\begingroup$ It's actually a hidden step when one does second quantization. Obviously, you don't really quantize twice, there is only the same good old quantum theory which you now apply to fields. What is not made explicit is the step where you consider a single particle Schrodinger equation as a classical field equation, this is an unquantization step :) $\endgroup$– Count IblisCommented Feb 7, 2016 at 18:25
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$\begingroup$ Look here: physics.stackexchange.com/questions/32112/… $\endgroup$– Name YYYCommented Feb 7, 2016 at 18:25
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$\begingroup$ It's called "decoherence". $\endgroup$– CuriousOneCommented Feb 7, 2016 at 20:57
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$\begingroup$ Look here: physics.stackexchange.com/questions/61569/… $\endgroup$– Cosmas ZachosCommented Apr 5, 2016 at 14:04
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2 Answers
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The term "dequantization" is used in other domains, and apparently in this context (e.g. in the preface to Quantum-Classical Correspondence: Dynamical Quantization and the Classical Limit, Bolivar, 2004, or in Variational approach to dequantization, Mosna et al., 2006).
I do believe the question might deserve more context, in other words is the question well-defined? There is a discussion in Classical Limit of Quantum Mechanics, and the beginning of Decoherence and the Classical Limit of Quantum Mechanics states that:
There is also an enormous amount of mathematical work, called semiclassical analysis or, in more modern terms, microlocal analysis (see, e.g., A. Martinez: An Introduction to Semiclassical and Microlocal Analysis, Bologna (2001)), in which the limit $\hbar \to > 0$ of Schr¨odinger evolutions is rigorously studied
and then asks
What is the relevant physical quantity whose convergence “in the classical limit” asserts in a satisfactory way that the classical world arises?
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2$\begingroup$ The transition from quantum mechanics to classical behavior doesn't occur because of the limit $\hbar \to 0$. That's an old falsehood that shouldn't be taught any longer. Decoherence doesn't require any such transition and it can be shown that the limit is discontinuous. $\endgroup$ Commented Feb 7, 2016 at 20:55
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1$\begingroup$ @CuriousOne: Why do you not write another answer then? $\endgroup$– asmaierCommented Feb 8, 2016 at 20:08
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Even in the old quantum theory, prior to 1925, to transition to the classical limit, known as the Bohr Correspondence principle, one doesn't let h -->0, but instead n --> Infinity.
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$\begingroup$ Bohr said, that the angular momentum should be multiples of Planck's constant: $L = n\hbar$. So if $L$ is taken as a constant taking the quantum number $n \rightarrow \infty$ basically implies $\hbar \rightarrow 0$ . Doesn't that mean that both statements are basically equivalent? $\endgroup$– asmaierCommented Feb 8, 2016 at 15:08