The numerical bootstrap method has been applied to solve eigenvalue problems in quantum mechanics. In this talk, I will give an overview of this method and its recent developments mainly in one-dimensional quantum mechanics. In particular, I will show that the bootstrap method can be regarded as a method for deriving eigenvalues using (an extension of) uncertainty relations. I will also show that the bootstrap method can derive exact results in solvable systems. This is a characteristic feature of the bootstrap method that is not found in other numerical analyses.