量子力學 Quantum

Science    Yoshio    Apr 2nd, 2024 at 8:00 PM    8    0   

量子力學

Quantum

量子力學是一個能用來解釋微觀世界的理論,其中的薛丁格方程式(Schrödinger Equation)就像是牛頓定律的 F=ma,然而牛頓定律(古典力學)沒辦法完全適用於如原子、電子、中子、質子這般微小的東西,而量子力學提供了我們一個能夠預測這些微小粒子行為的理論。

在氫原子中,電子有許多的軌域(1s, 2s, 2p, 3s, 3p, 3d, ……),並對應到各個能階,這些能階是離散的、非連續的。並且,只有處於這些特定的能量(或稱作能階,因為像台階一樣一階一階的)時,電子才是穩定的環繞在原子核周圍。




薛丁格方程式

Schrödinger equation

Beginning in the early 20th century, physicists began to acknowledge that matter--much like electromagnetic radiation--possessed wave-like behaviors. While electromagnetic radiation were well understood to obey Maxwell's Equations, matter obeyed no known equations.


In 1926, the Austrian physicist Erwin Schrödinger formulated what came to be known as the Schrödinger Equation:

\[i\hbar\dfrac{\partial}{\partial t}\psi(x,t)=\dfrac{-\hbar}{2m}\nabla^2\psi(x,t) +V(x)\psi(x,t)\]

time-independent Schrödinger equation

\[E\psi(x)=\frac{-\hslash^2}{2m}\frac{d^2\psi(x)}{dx^2}+V(x)\psi(x)\]