为什么我们无法推导薛定谔方程？

今天有典型的中式网络思维者给我短信号称他知道如何推导薛定谔方程。原本对这种中式网络专业人士的标致性的轻佻思维应该置之一笑而已，但正好在网上碰上一则讲解为什么我们无法推导薛定谔方程的帖子，就将之转贴于此 （https://www.quora.com/Why-we-say-that-we-cant-derive-Schrodinger-equation）：

Why we say that we can't "derive" Schrodinger equation?

Schrodinger's equation cannot be derived. It was thought up using logical arguments and so far it has seemed to work experimentally.

The equations is essentially a re-write up for energy conservation:

E=T+V

Where T

is the Kinetic Energy and V

is the potential. However, to be more explicit we must work with operators (if you are unsure what operators are I suggest you look them up; this will give you a better understanding of what's going on).

The KE for a particle is given by the KE Operator:

T^=−?22m∂2∂x2

This comes from the momentum operator of the particle/wave p^=−ih∂/∂x

. You use this in the analogous classical mechanics equation for KE to obtain T^

(Try doing this as an exercise).

So now we are left with just putting it all together. The first equation turns into:

−?22m∂2Ψ∂x2+V(x)Ψ=EΨ

And we define the Hamiltonian H^ as:

H^=−?22m∂2∂x2+V(x)

Thus:

H^Ψ=EΨ

 

注：其实我们之所以不能推导薛定谔方程的原因比此贴所解释更深刻。我在给该网络思维人士的回帖中对其背后的哲学原因进行了解释。这里就不赘述。上面这个短贴已经把基本的要点做了一些解释。

[慕容青草]

本文所提到的中式网络思维其实也并不局限于中文网站，只不过在中文网站表现得比较突出。在那些有着所谓的Moderator的英文论坛也常会出现这种现象，他们常会把自己的课本上读到的内容当作是不可置疑的金科玉律，而忽略了那些内容背后所存在的争议性和近似性。这样的思维方式常使得他们会把自己原本一知半解并不知其所以然的理论拿来当作教训他人的依据，显得极为浅薄。如果说那些论坛的Moderator们那样做是有着金钱厉害关系（如果他们的Moderator职位是领薪的话）的使然，那么中文网站上表现出类似的思维的状况除了也可能有背后的金钱关系（如果是专业网络人士的话）之外，更多则是显摆自己曾经是理工科的高才生，是一种对失去的旧梦的追思。。。