為什麽我們無法推導薛定諤方程？

今天有典型的中式網絡思維者給我短信號稱他知道如何推導薛定諤方程。原本對這種中式網絡專業人士的標致性的輕佻思維應該置之一笑而已，但正好在網上碰上一則講解為什麽我們無法推導薛定諤方程的帖子，就將之轉貼於此 （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：其實我們之所以不能推導薛定諤方程的原因比此貼所解釋更深刻。我在給該網絡思維人士的回帖中對其背後的哲學原因進行了解釋。這裏就不贅述。上麵這個短貼已經把基本的要點做了一些解釋。

[慕容青草]

本文所提到的中式網絡思維其實也並不局限於中文網站，隻不過在中文網站表現得比較突出。在那些有著所謂的Moderator的英文論壇也常會出現這種現象，他們常會把自己的課本上讀到的內容當作是不可置疑的金科玉律，而忽略了那些內容背後所存在的爭議性和近似性。這樣的思維方式常使得他們會把自己原本一知半解並不知其所以然的理論拿來當作教訓他人的依據，顯得極為淺薄。如果說那些論壇的Moderator們那樣做是有著金錢厲害關係（如果他們的Moderator職位是領薪的話）的使然，那麽中文網站上表現出類似的思維的狀況除了也可能有背後的金錢關係（如果是專業網絡人士的話）之外，更多則是顯擺自己曾經是理工科的高才生，是一種對失去的舊夢的追思。。。