Precision Tests of Quantum Mechanics

It is proposed to set stringent limits on possible nonlinear corrections to ordinary quantum mechanics by searching for the detuning of resonant transitions. A suggested nonlinear generalization of quantum mechanics is used to show that such detuning would be expected in the rf transition in ${}_{}{}^9{}_{}{}^{}\mathrm{Be}_{}^{+}{}_{}{}^{}$ ions that is used to set frequency standards. Measurements at the National Bureau of Standards already set limits of order ${10}^{-21\mathrm{}}$ on the fraction of the energy of the ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$ nucleus that could be due to nonlinear corrections to quantum mechanics, with good prospects of improving this by 2-3 orders of magnitude.