L.I. Mandel'shtam’s scientific contributions

... Heisenberg put forward this principle for the canonical conjugated variables of momentum and position in 1927 [22], which was later generalized as an inequality by Kennard for any arbitrary wave function [23]. In 1945, Mandelshtam and Tamm derived a similar nonrelativistic uncertainty principle between energy and time in the form of the Mandelshtam-Tamm inequality [24]. In this latter inequality, time still remains as an independent privileged variable. ...

Reference:

The Uncertainty Principle and the Minimal Space–Time Length Element

... As was shown in [5], distance S traveled by the useful signal modulating SSWs with frequency f 0 in such a structure along axis y with no distortions (the shape of the signal is preserved) is limited by the condition (1) which includes modulus U of the vector of the group velocity of a modulated wave, modulated wavelength λ 0 = 2π/k y0 , and derivative ∂U/∂λ calculated at λ = λ 0 . 2 2 y k ∂ ω ∂ It is also convenient to write condition (1) in the form S S cr , where critical distance S cr is calculated using the formula [6] (2) which includes the first and second derivatives of the dispersion dependence for the considered structure. ...

Reference:

Undistorted Transmission of a Useful Signal by Surface Spin Waves in a Metal–Ferrite–Dielectric–Metal Structure