Solution of the Schroedinger equation of the complex manifold CPn

Passing from the CPn = SU(n + 1)/U(n) Lagrangian in Kaehler form, to the Hamiltonian in terms of polar coordinates, this paper describes the solutions of the CPn Schroedinger equation, whose energy eigenspaces carry the irreducible representations (λ, 0n-2, λ), λ = 0, 1, 2, ..., of SU(n + 1) in highest weight notation. A full account is given of the U(n) structure of these eigenspaces, and of how this emerges within our solution of the Schroedinger equation by separation of variables. Explicit solutions of the radial equation, which give rise to the derivation of spectrum and energy eigenspace details, are presented for λ = 1, 2, and related to Jacobi polynomials