Hamiltonians with su(2) and su(3) symmetry and orthogonal polynomials

par Julien Gaboriaud (Univ. Montréal)

jeudi 6 juil. 2023, 11:00 → 12:00 Europe/Paris

Petit Amphi (LAPTh)

In quantum mechanics we diagonalize a Hamiltonian in order to solve Schrödinger’s equation. What if the Hamiltonian has symmetries, such as su(2) or su(3)? Then, there exist multiple bases which diagonalize the Hamiltonian and we can find the change of basis coefficients between these various bases. In this introductory talk, I will show how some remarkable families of orthogonal polynomials appear when studying these coefficients: the Krawtchouk and Racah polynomials.