Overcoming Infinity

R. Guardiola

Vadim Cheianov

A transformation of variables overcomes fundamental difficulties in formulating a unified theory of one-dimensional quantum fluids.

Pieter Naaijkens

Justin Mullins

L. M. Arévalo Aguilar, Fernando Velasco Luna, Carlos Ignacio Robledo-Sánchez +1 more

This paper explains and illustrates the application of the evolution operator method to solve problems in quantum mechanics. Currently, this method has been proposed as a useful way to overcome some misconceptions in quantum mechanics. To illustrate the method, we apply it to analyze and study the case of a quantum system inside an infinite square well potential (ISWP), and compare this result with that obtained using the traditional method. Also, we analyze the collapse and revival phenomenon in the ISWP. In this case, we argue that the usual approach to studying this effect requires one to extend the function's domain to infinity; however, there has not been any assurance that this extension preserves the self-adjointness of the Hamiltonian operator. The self-adjointness of the Hamiltonian operator is a vital requirement to guarantee the uniqueness of the Schrödinger equation's solution.

Koenraad M. R. Audenaert

We introduce the telescopic relative entropy (TRE), which is a new regularisation of the relative entropy related to smoothing, to overcome the problem that the relative entropy between pure states is either zero or infinity and therefore useless as a distance measure in this case. We study basic properties of this quantity, and find interesting relationships between the TRE and the trace norm distance. We then exploit the same techniques to obtain a new and shorter proof of a lower bound on the relative Renyi entropies in terms of the trace norm distance, $\traceρ^{1-p}σ^p \ge 1-(||ρ-σ||_1)/2$.