  We give a short review of known exact inequalities that can be interpreted as
"energy-time" and "frequency-time" uncertainty relations. In particular we
discuss a precise form of signals minimizing the physical frequency-time
uncertainty product. Also, we calculate the "stationarity time" for mixed
Gaussian states of a quantum harmonic oscillator, showing explicitly that pure
quantum states are "more fragile" than mixed ones with the same value of the
energy dispersion. The problems of quantum evolution speed limits, time
operators and measurements of energy and time are briefly discussed, too.
