Expanding Hermitian operators in a basis of projectors on coherent spin states

Abstract

The expectation values of a hermitean operator A in (2s+1)(2s+1) specific coherent states of a spin are known to determine the operator unambiguously. As shown here, (almost) any other (2s+1)(2s+1) coherent states also provide a basis for self-adjoint operators. This is proven by considering the determinant of the Gram matrix associated with the coherent state projectors as a Hamiltonian of a fictitious classical spin system.