∆E ∆t ≥ ħ Time is a parameter, not an observable. ∆t is some timescale over which the expectation value of an operator changes. For example, an electron's angular momentum in a hydrogen atom decays from 2p to 1s. These decays are relativistic, however the uncertainty principle is still valid, and we can use it to estimate uncertainties. The lifetime of hydrogen in the 2p state to decay to the Is ground state is 1.6 x 10-9 s. Estimate the uncertainty ∆E in energy of this excited state. What is the corresponding linewidth in angstroms?

∆E ∆t ≥ ħ Time is a parameter, not an observable. ∆t is some timescale over which the expectation value of an operator changes. For example, an electron's angular momentum in a hydrogen atom decays from 2p to 1s. These decays are relativistic, however the uncertainty principle is still valid, and we can use it to estimate uncertainties. The lifetime of hydrogen in the 2p state to decay to the Is ground state is 1.6 x 10-9 s. Estimate the uncertainty ∆E in energy of this excited state. What is the corresponding linewidth in angstroms?