// ＜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…

// ＜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…

＜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…