This blog aims to trace historical and scientific origins of Schrödinger equation, focusing on its development from 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) is a method used to fine-tune large language models by directly optimizing their parameters based on human feedback. DPO effectively addresses the challenges associated with supervised fine-tuning during the advanced stages of reinforcement learning. The concept behind DPO is to integrate preference data directly into the model’s training process, adjusting the model’s parameters to increase the likelihood of generating outputs similar to those preferred by humans....
Introduction Mathematics and science are deeply interconnected, with math providing the founfation for scientific theories. However, there exists an huge gap within mathematics—a gap that ensures we will never touch complete certainty. Certain true statements remain unprovable, potentially challenging our belief in scientific discoveries. Historical context Russell’s paradox and formalism In 1874, Georg Cantor introduced the concept of sets, and a branch of mathematics named set theory, which studies well-defined collections of things....
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...