This blog aims to trace the historical and scientific origins of the Schrödinger equation, focusing on its development from the hydrogen atom model. Initially, attempts were made to derive a relativistic equation for the hydrogen atom, but eventually, a nonrelativistic approach was adopted instead. By combining principles from Hamiltonian mechanics, Erwin Schrödinger successfully formulated the final Schrödinger equation. Through this exploration, we could gain a deeper understanding of the scientific advancements and conceptual breakthroughs that led to the creation of the Schrödinger equation, shedding light on its profound impact on the field of quantum mechanics....
Introduction Direct Preference Optimization (DPO) fine-tunes LLMs using human feedback directly, bypassing the traditional reinforcement learning pipeline. Unlike methods that require training a separate reward model, DPO integrates preference data straight into the optimization objective—making it both simpler and more stable. Why does this matter? In later stages of RL training, the gap between "preferred" and "rejected" responses becomes vanishingly small. Supervised Fine-Tuning (SFT) alone can inadvertently amplify rewards for subtly incorrect outputs....
Introduction The bedrock of science is not observation—not even mathematics. It is axioms. Gödel proved that any formal system complex enough to encode arithmetic contains truths it cannot prove. Cubitt et al. later showed that even whether a quantum system has an energy gap can be undecidable. These results are not abstract curiosities; they impose fundamental limits on what science can ever know. This blog explores those limits and what they mean for how we should think about scientific truth....
背景介绍 孤子的发现应追溯到1834年的夏日，英国科学家 J.S.Russel 骑马正沿着一条运河岸道旅行，偶然发现在狭窄的河床中行走的船突然停止前进，被船体带动的...
从霜花到海岸线，自然界中分形无处不在，近现代物理学中同样不断能够找到分形的影子. 本文回顾了通过类比 Weierstrass 函数，可以从量子气体中寻求到相应的动力学...