Checking if Bose-Einstein Condensation can occur in 1D and 2D for free particles using periodic boundary conditions — and why the density of states is the key.

A practical guide to applying for Physics Ph.D. programs in Canada and Germany — where to look, how to contact supervisors, and how to prepare your documents.

When [A, B] = c is a constant, a slick ODE trick unlocks three powerful operator identities used throughout quantum mechanics.

Exploring how the quantum mechanical correlation function C(t) relates to the classical limit of a Gaussian state with width σ_ω.

Pure states, mixtures, ensemble averages, cyclic trace, and the von Neumann equation — all the core properties of the density operator worked out explicitly.