Quantum mechanics applies at all scales from "summary" of The Principles of Quantum Mechanics by P. A. M. Dirac
The principles of quantum mechanics have been found to apply not only to atomic phenomena but also to macroscopic systems. This is a most striking fact, and one of the reasons for it is that the quantum equations involve Planck's constant h, which is exceedingly small in ordinary units. As a result, the quantum effects tend to be very small and difficult to observe except in delicate laboratory experiments.
However, it is possible for these effects to become significant in systems involving a large number of particles, such as a crystal. In such cases, the effects of individual particles can combine together in such a way as to produce a noticeable result on a macroscopic scale. This is why quantum mechanics can be relevant not only to the microscopic world but also to the world of everyday experience.
Furthermore, as the size of the system under consideration increases, the quantum effects tend to become less pronounced, and the behavior of the system approaches that predicted by classical mechanics. This is because the quantum effects are proportional to powers of h, and as h becomes smaller relative to the other quantities in the problem, these effects become negligible.
Nevertheless, even in macroscopic systems where quantum effects are small, they can still play an important role in determining the properties of the system. For example, the electrical conductivity of a metal at low temperatures can only be explained by quantum mechanical considerations. Therefore, although quantum effects may be hard to observe directly in large systems, they can still have a significant impact on the behavior of those systems.
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