Quantum Particle on Dual Weight Lattice in Even Weyl Alcove

Abstract Even subgroups of affine Weyl groups corresponding to irreducible crystallographic root systems characterize families single-particle quantum systems. Induced by primary and secondary sign homomorphisms the groups, free propagations particle on refined dual weight lattices inside rescaled even alcoves are determined Hamiltonians tight-binding types. Described hopping functions, amplitudes particle’s jumps lattice neighbours together with diverse boundary conditions incorporated through operators into resulting dual-weight Hamiltonians. Expressing eigenenergies via weighted sums orbit associated time-independent Schrödinger equations exactly solved applying discrete Fourier–Weyl transforms. Matrices specifications complementary detailed for C 2 G models.