Heisenberg picture formulation of matrix mechanics in an arbitrary basis, in which the Hamiltonian is not necessarily diagonal. It further serves to define a third, hybrid, picture, the interaction picture. In the Heisenberg picture of quantum mechanics the state vectors, |"ψ("t")"〉, do not change with time, while observables satisfy where is the Hamiltonian and <nowiki>[•,•]</nowiki> denotes the commutator of two operators (in this case and ). Taking expectation values automatically yields the Ehrenfest theorem, featured in the correspondence principle. By the Stone–von Neumann theorem, the Heisenberg picture and the Schrödinger picture are unitarily equivalent, just a basis change in Hilbert space. In
Astroparticle physics Astroparticle physics Astroparticle physics, also called particle astrophysics, is a branch of particle physics that studies elementary particles of astronomical origin and their relation to astrophysics and cosmology. It is a relatively new field of research emerging at the intersection of particle physics, astronomy, astrophysics, detector physics, relativity, solid state physics, and cosmology. Partly motivated by the discovery of neutrino oscillation, the field has undergone rapid development, both theoretically and experimentally, since the early 2000s. The field of astroparticle physics is evolved out of optical astronomy. With the growth of detector technology came the more mature astrophysics, which involved multiple