Exactly Solvable Quantum Mechanics

A comprehensive review of exactly solvable quantum mechanics is presented with the emphasis of the recently discovered multi-indexed orthogonal polynomials. The main sub-jects to be discussed are the factorised Hamiltonians, the general structure of the solution spaces of the Schrödinger equation (Crum’s theorem and its modifications), the shape invari-ance, the exact solvability in the Schrödinger picture as well as in the Heisenberg picture, the creation/annihilation operators and the dynamical symmetry algebras, coherent states, various deformation schemes (multiple Darboux transformations) and the infinite families of multi-indexed orthogonal polynomials, the exceptional orthogonal polynomials, and de-formed exactly solvable scattering problems. PACS numbers: 03.65.-w, 03.65.Ca, 03.65.Fd, 03.65.Ge, 03.65.Nk, 02.30.Ik, 02.30.Gp 1