证明△(uv)=u△v+v△u+2▽u•▽v 关于哈密顿算子的,矢量分析类的体,
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![证明△(uv)=u△v+v△u+2▽u•▽v 关于哈密顿算子的,矢量分析类的体,](/uploads/image/z/6517050-42-0.jpg?t=%E8%AF%81%E6%98%8E%E2%96%B3%28uv%29%3Du%E2%96%B3v%2Bv%E2%96%B3u%2B2%E2%96%BDu%26%238226%3B%E2%96%BDv+%E5%85%B3%E4%BA%8E%E5%93%88%E5%AF%86%E9%A1%BF%E7%AE%97%E5%AD%90%E7%9A%84%2C%E7%9F%A2%E9%87%8F%E5%88%86%E6%9E%90%E7%B1%BB%E7%9A%84%E4%BD%93%2C)
证明△(uv)=u△v+v△u+2▽u•▽v 关于哈密顿算子的,矢量分析类的体,
证明△(uv)=u△v+v△u+2▽u•▽v 关于哈密顿算子的,矢量分析类的体,
证明△(uv)=u△v+v△u+2▽u•▽v 关于哈密顿算子的,矢量分析类的体,
△(uv)=(ið^2/ðx^2+jð^2/ðy^2+kð^2/ðz^2)(uv),而 ð^2/ðx^2=ð(u*ðv/ðx+vðu/ðx)/ðx=uð^2v/ðx^2+vð^2u/ðx^2+2ðu/ðx*ðv/ðx),同理ð^2/ðy^2=uð^2v/ðy^2+vð^2u/ðy^2+2ðu/ðy*ðv/ðy),ð^2/ðz^2=uð^2v/ðz^2+vð^2u/ðz^2+2ðu/ðz*ðv/ðz).所以△(uv)= u(ið^2v/ðx^2+jð^2v/ðy^2+kð^2v/ðz^2)+v(ið^2u/ðx^2+jð^2u/ðy^2+kð^2u/ðz^2)+2(iðu/ðx*ðv/ðx+jðu/ðy*ðv/ðy+kðu/ðz*ðv/ðz)=u△v+v△u+2(iðu/ðx+jðu/ðy+kðu/ðz)*(iðv/ðx+jðv/ðy+kðv/ðz)=u△v+v△u+2▽u•▽v.