Comment on "Quantitative Condition is Necessary in Guaranteeing the Validity of the Adiabatic Approximation" [arXiv:1004.3100]

TL;DR

This paper critiques a recent claim that the traditional adiabatic condition is necessary, identifying errors and overly restrictive assumptions in the original proof.

Contribution

It challenges the validity of the previous proof, clarifying misconceptions about the necessity of the adiabatic condition in quantum mechanics.

Findings

Identifies mistakes in the original proof

Highlights over-strong constraints in the previous work

Questions the necessity of the traditional adiabatic condition

Abstract

Recently, the authors of Ref.1[arXiv:1004.3100] claimed that they have proven the traditional adiabatic condition is a necessary condition. Here, it is claimed that there are some mistakes and an artificial over-strong constraint in [1], making its result inconvincible.