Bethe Quantum Research Articles

Bohr's stopping-power formula derived for a classical free-electron gas

Bohr's centenary stopping-power formula is rederived for a free electron gas (FEG) system within the framework of nonrelativistic classical mechanics. A simple and more concise expression for the stopping power of charged particles in FEG is demonstrated on classical grounds. Using semiclassical arguments and the Euler-Maclaurin well-known mathematical formula, Bloch's correction that links Bethe's quantum theory to Bohr's classical model is also recovered. The proposed semiclassical stopping-power formula contains the main physical ingredients for a general stopping formula applicable for different systems and energies and facilitates computational calculations.

Bethe's quantum numbers and rigged configurations

We propose a method to determine the quantum numbers, which we call the rigged configurations, for the solutions to the Bethe ansatz equations for the spin-1/2 isotropic Heisenberg model under the periodic boundary condition. Our method is based on the observation that the sums of Bethe's quantum numbers within each string behave particularly nicely. We confirm our procedure for all solutions for length 12 chain (totally 923 solutions).