aakashl

Semiclassics is a regime where things look quantum but can be computed classically. I talk about this in what follows based on this paper by Dirac.

The point of this post is to demonstrate that semiclassics doesn’t need any appeal to quantum dynamics, only quantum ontology. It is of course important though that regular quantum mechanics deforms into semiclassics which it does via . I demonstrate this deformation via the 2 classical formulations of quantum mechanics and then I present Dirac’s result where we quantize just the ontology, leaving the evolution classical. The demonstrations are independent so you can skip straight to Dirac.

In any case, the ultimate result is that we need only consider Hamilton’s principal function from Hamilton-Jacobi theory to understand what is happening semiclassically. This also shows that quantum mechanics is not much more than geometric optics of wavefunctions given the well-known correspondence between the principal function and optical path length.