I guess the following quesition on our problem set summarizes our study of linear algebra, up to tensor product. (3) Suppose that V and W are finite-dimensional vector spaces. The set Hom(V,W) = {T : V -> W : T is linear} forms a vector sp…

今日はよく寝た。十二時におきて四時まで適当にごろごろし、七時までまたねた。昼を逃すと何かさびしい気がする。昨日はひとちゃんの声が聞けてとてもうれしかった。また電話しよう。 数学と物理はとりあえずほってある。物理はさっき少し始めた。春休みはと…

やっと春休みが始まった。二学期は一学期以上に数学と物理を面白いと感じるが、体力的には疲れている。Maybe I just miss my girlfriend in Japan. Maybe. この休みの間に １ 夏の願書を書くこと、 ２ 線形代数の復習、 ３ 量子力学を読み進めること、 ４ 化…

What is the mechanism for Van der waals force? The answer to the question, "how can I stabilize n electrons on a sphere the most?" turned out to be very difficult. Tom and I thought we could solve the problem by treating it as minimization…

In order to understand one chapter of a physics book, one needs to solve numerous problems and try to approach the same problem from many different angles. Try not to hurry and enjoy one problem at a time, then, I should be able to underst…

Apparently, the community of physics is a very nice place to be. I hope I can be one of those people one day and enjoy physics to the full extent. The question below suggests that how "comfortable" or energetically favorable or mathematica…

Question: if you have n points on a sphere and want to spread them out as uniformly as possible, how would you do it? (n \in N). Is this problem equivalent to this problem?: if you have n electrons connected to the center of sphere with st…

The idea of category is very interesting. Mathematicians' way of understanding concepts is truly amazing.

If B = [T;\beta', \gamma'] and A = [T; \beta, \gamma], then there exists Q and R such that B = R A Q^{-1}. It seems the definition of R and Q have to be perverse in order to make the matrices work in a reasonable way.

数学や物理ではパズル（問題）を解く能力とシステムを理解する能力の両方が必要とされる。どちらもとても大切であり、双方が身について初めて、僕らは各科目の理解を深めることができるものであるから、二つを分けることに意味はあまりない。具体的にいえば…

Problem 2.47 of Griffiths. How does the wave function(psi function) look like as b \to infty? I found an answer in Caltech 2b website. I was rather surprising result.

1. Why does Enatiomer rotate the polarity of light? How does an molecule (or electrons localized at a certain place) interact with electoric field and magnetic field? 2. Equilibrium constant does not depend on whether we use catalyst or no…