State-independent uncertainty relations from eigenvalue minimization

We consider uncertainty relations that give lower bounds to the sum of variances. Finding such lower bounds
is typically complicated, and efficient procedures are known only for a handful of cases. In this paper, we present
procedures based on finding the ground state of appropriate Hamiltonian operators, which can make use of the
many known techniques developed to this aim. To demonstrate the simplicity of the method, we analyze multiple
instances, that involve two or more observables, both bounded and unbounded.