// ＜Complete Normalized Orthogonal System＞完全正規直交系(正規直交基底) The j-th wave function is expressed by complete normalized orthogonal system as follows.(j番目の波動関数は完全正規直交系を用いて次のように表される。) \begin{eqnarray}…
// ＜Time-independent Hamiltonian＞ Schrödinger's Wave Equation is described as follows. \begin{eqnarray}i\hbar\frac{\partial}{\partial t}\Psi &=&\hat{H}\Psi\end{eqnarray} ] ] ] ] ] ] ] Schrödinger's Wave Equation is described as follows w…
// ＜Linear Differential Equation part 2＞ Linear differential equation can be solved as below.(線形微分方程式は下記のように解くことができる。) \begin{eqnarray}\prod_{i=0}^k\left(\frac{d}{dx}-\lambda_i\right)y&=&0\notag \\ \left(\frac{d}{d…
// ＜Linear Differential Equation＞ Linear differential equation can be solved as follows.(線形微分方程式は次のようにして解くことができる。) \begin{eqnarray}\left(\frac{d}{dx}-\lambda\right)^{k}y&=&0\notag\\\left(\frac{d}{dx}-\lambda\right…
// ＜Linear Differential Operator＞ A linear combination of differential operators is described as below. \begin{eqnarray}\sum_{i=0}^na_i\left(\frac{d}{dx}\right)^i\end{eqnarray} Then, the next formula is true. \begin{eqnarray}\sum_{i=0}^n…
// ＜Wave Equation＞ Wave equation in 3 dimensions is described as below. \begin{eqnarray}\frac{\partial^2u}{\partial t^2} &=& v^2\left(\frac{\partial^2u}{\partial x^2}+\frac{\partial^2u}{\partial y^2}+\frac{\partial^2u}{\partial z^2}\righ…
// ＜Wave Equation＞ Wave equation in one dimension is described as below. \begin{eqnarray}\frac{\partial^2u}{\partial t^2} &=& v^2\frac{\partial^2u}{\partial x^2} \end{eqnarray} Here, is the displacement of the wave at position in time , …
// ＜Simple Harmonic Oscillation＞ Newton's equation of motion in one-dimension is described as below. \begin{eqnarray} m\frac{d^2x}{dt^2} &=& F \end{eqnarray} Here, we assume the situation that the point mass is connected to the spring, t…
＜Defeat＞ I was very excited in Rio 2016 Olympics by the fact that TAKAHASHI MATSUTOMO badminton pair (TAKA-MATSU pair) won the gold medal. Especially, getting 5 consective points from the situation losing 16-19 is still fresh in my memor…
＜Celebration＞ I went to my parents' home for the first time in 2 months to celebrate my sister's birthday. My family decide to eat out before and after my family member's birthday.We went to washoku sato near home and ate shabu-shabu, su…
＜Newton's Equation of Motion＞ Newton's Equation of Motion is described as below \[m\frac{d^2{\boldsymbol r}}{dt^2} = {\boldsymbol F} \] Here, is the position vector of point mass whose mass is m, and is the force vector acting on the poi…
＜Long time, No hear＞ Never for a long time have I heard the Japanese popular song "LOVE LOVE LOVE" which was released by DREAMS COME TRUE in 1995. These few days I heard it many times because it has been used as BGM in SUBARU TV-commerci…
＜UNLUCKY＞ If the weather in Suzuka had permitted, I would have taken pictures in which blue sky had many colorful balloons. According to official homepage, it seems that balloons flew up only in the 1st day morning out of 3 days(from 16 …
＜SELF-INTRODUCTION＞ I am a chemical researcher who has worked in Japanese small-to-medium-sized enterprise for 3 years and 5months (at September, 2016). ＜PURPOSE＞ The purpose of the blog is to improve my English ability by recording da…
