Physvillain

In classical physics, all physical quantities were considered to satisfy the commutation relation. For example, in classical mechanics, two quantities $A(x,p)$ and $B(x,p)$ have the commutative property of multiplication. But in the quantum mechanics, the commutation of $A$ and $B$ is not zero in general. \begin{equation}\tag{1} \left[ A(x, p), B(x, p) \right] \neq 0. \end{equation} The history ..

이 글은 2019.12.14에 작성되어 아직까지 TBC임. 원본 : physvillain.blogspot.com/2019/12/n-dimensional-radial-momentum-operator.html free particle의 Hamiltonian operator을 생각하자. $$H=-\frac{\hbar^2}{2m}\vec{\nabla}^2$$3차원 spherical coordinate에서 이것은 다음과 같이 써진다. $$H=-\frac{\hbar^2}{2m}\left( \frac{1}{r^2}\partial_r r^2 \partial_r \right)+\frac{\vec{L}^2}{2mr^2}$$그런데 $\frac{1}{r^2} \partial_r r^2 \partial_r = \frac{1}{..