Asymptotic relation for the quantum entropy of momentum in energy eigenstates

Jorge Sánchez-Ruiz

Vladimír Majerník, Tomáš Opatrný

We calculated the Shannon entropy of position and momentum for the stationary quantum states of the harmonic oscillator as a function of its energy and determined the corresponding entropic uncertainty relations for them. We found an approximate phenomenological function for the dependence of position and momentum entropies on the large quantum numbers and the corresponding asymptotic entropy - energy relation for the stationary harmonic oscillator. We also studied the time evolution of the position and momentum entropies of the non-stationary harmonic oscillator for the coherent states, squeezed vacuum and Schrödinger cat states.

Göran Lindblad

Mark W. Coffey

The classical and semiclassical position entropies for the three-dimensional Coulomb problem are obtained explicitly for all values of angular momentum, without recourse to asymptotic expansions. The analytic results relate the classical period of the motion, total energy, position entropy and dependence upon the principal quantum number n . It is demonstrated that the position entropy varies with energy E as ln| E | −1 .

Eric Young, Peter B. Shaw, George Whitfield

We consider an electron interacting with acoustic phonons through the deformation potential in one dimension. By using a trial state that is an eigenfunction of momentum we show that at high momentum the velocity of the polaron approaches the speed of sound. Since the trial state that we are using is an upper bound for each momentum, the more usual quadratic energy-momentum relation is clearly eliminated.

Shigeo Akashi