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。

所有跟帖： 

• 薛定諤的貓和方程有什麽聯係嗎？：） -盈盈一笑間- ♀ (0 bytes) () 07/29/2021 postreply 17:12:07