# 2018年 12月 の投稿一覧

The Schrödinger Equation

$$iħ\frac{∂}{∂t}Ψ({\bf r},t)=-\frac{ħ^2}{2m}∇^2Ψ({\bf r},t)$$

Using Hamiltonian,

$$iħ\frac{∂}{∂t}Ψ({\bf r},t)=\hat{H}Ψ({\bf r},t)$$

In this post, after deriving the Schrödinger Equation equation, we obtain the momentum operator.

Observe moving objects near the light speed from a static system. Then, the object looks shorter than the original length (the length when the object stopped). This phenomenon is called Lorentz contraction.

Let $L_0$ be the length of the bar when the object is stopped and $L$ the length of the moving bar observed from the static system. Then, the following relationship holds between the two. However, it is assumed that the system S’ is moving at a speed V in the x direction with respect to the system S and the bar is moving with the system S’.

\begin{eqnarray} L&=&L_0\sqrt{1-\frac{V^2}{c^2}}\\&=&L_0\sqrt{1-β^2} \end{eqnarray}

Kepler’s law is what concerning the movement of a planet. If you can master this rule, you can easily think about the movement of the planet. And in order to think about this, it is the quickest to introduce the motion equation of two-dimensional polar coordinates. In this post, I’ll introduce Kepler’s law and prove it.

The universal gravitational force working between a particle of mass $m$ and a particle of mass $M$ is expressed as follows when the distance between the particles is $r$.

$$f(r)=-G\frac{mM}{r^2}$$

$$G=6.672 \times 10^{-11}[N･m^2/kg^2]$$

$G$ is called gravitational constant.

In quantum mechanics, use bra vector  $<a|$ and ket vector $|a>$. What are the advantages of introducing them?