Deriving the transfer matrix connecting incoming and outgoing WKB amplitudes across a general potential barrier, and extracting the tunneling transmission coefficient.

Deriving the explicit matrix form and normalization of the spin eigenstates |n; +⟩ for a general unit vector n̂ defined by spherical angles θ and φ.

A deep dive into why "Hermitian" operators aren’t always self-adjoint, and why this matters for the momentum operator in quantum mechanics.

How to apply to IPSP Leipzig as an international student — HEQ requirements, Studienkolleg, JEE-Advanced eligibility, and the Uni-assist application process.

A detailed look at the directed polymer on a square lattice, counting microstates and calculating typical deflection using the partition function.