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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Look here: http://physics.stackexchange.com/questions/32112/classical-limit-of-quantum-mechanics – Name YYY Feb 07 '16 at 18:25
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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 :) – Count Iblis Feb 07 '16 at 18:25
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It's called "decoherence". – CuriousOne Feb 07 '16 at 20:57
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Look here: http://physics.stackexchange.com/questions/61569/hbar-rightarrow-0-in-quantum-mechanics – Cosmas Zachos Apr 05 '16 at 14:04
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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?
Laurent Duval
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2The 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. – CuriousOne Feb 07 '16 at 20:55
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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.
JQK
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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? – asmaier Feb 08 '16 at 15:08