一维薛定谔方程
−h22μ∂2ψ(x,t)∂x2+U(x,t)ψ(x,t)=ih∂ψ(x,t)∂t -\frac{h^2}{2\mu} \frac{\partial^2\psi(x,t)}{\partial x^2} +U(x,t)\psi(x,t) =ih\frac{\partial\psi(x,t)}{\partial t} −2μh2∂x2∂2ψ(x,t)+U(x,t)ψ(x,t)=ih∂t∂ψ(x,t)
三维薛定谔方程
−h22μ(∂2ψ∂x2+∂2ψ∂y2+∂2ψ∂z2)+U(x,y,z)ψ=ih∂ψ∂t -\frac{h^2}{2\mu}( \frac{\partial^2\psi}{\partial x^2} +\frac{\partial^2\psi}{\partial y^2} +\frac{\partial^2\psi}{\partial z^2} ) +U(x,y,z)\psi =ih\frac{\partial\psi}{\partial t} −2μh2(∂x2∂2ψ+∂y2∂2ψ+∂z2∂2ψ)+U(x,y,z)ψ=ih∂t∂ψ
定态薛定谔方程
−h22μ▽2ψ+Uψ=Eψ -\frac{h^2}{2\mu}\triangledown ^2\psi +U\psi =E\psi −2μh2▽2ψ+Uψ=Eψ
