Minimization of the expectation value of energy under the constraints imposed by the uncertainty principle can be a convenient method of solving quantum-mechanical problems.
@article{arxiv.1206.1576,
title = {A quantitative aspect of the Heisenberg uncertainty},
author = {A. K. Khitrin},
journal= {arXiv preprint arXiv:1206.1576},
year = {2012}
}