Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Can anyone provie me the proof of $Dq-qD=1$ where $D=\frac{\partial }{\partial q}$ refers to the differential operator?

Or if it's something special to quantum mechanics, why is it?

Is this following from $[\hat{q},\hat{p}] =i\hbar ~{\bf 1}$?

share|cite|improve this question
i think you mean to say D is the derivative operator, not any differential operator. – Prathyush Oct 18 '12 at 10:51
what's the difference between two? – RRRR Oct 18 '12 at 10:53
a differential operator can be anything like (d/dx)^2, but derivative operator is d/dx – Prathyush Oct 18 '12 at 11:15
up vote 5 down vote accepted

a hint

$$ Dxf(x)= f(x)+xDf(x) $$

$$ xDf(x) $$

take the diference and you get $ f(x) $ or $ 1.f(x)$

share|cite|improve this answer

$$[D,q]f(q)=Dqf(q)-qDf(q) =\frac{d}{dq}(qf)-\frac{qd}{dq}$$

$$\Rightarrow [D,q]f(q)=q \frac{df}{dq}+f \frac{dq}{dq}-q \frac{df}{dq}$$

$$\Rightarrow [D,q]f(q)=\frac{dq}{dq}=1$$

$$\Rightarrow [D,q]f(q)=f$$

Now,remove $f$ from both side,


share|cite|improve this answer
@Manikanta If you're going to LaTeXify, please do it thoroughly. If you want, use this tool to help you convert plain math to TeX. – Manishearth Nov 26 '12 at 15:43
Generally, we only provide hints to homework questions and not full answers--you may want to edit. (See homework policy) – Manishearth Nov 26 '12 at 15:46
I would ordinarily temporarily delete this, but it's an old question anyway so I'll just leave it here. ali, just keep the homework policy in mind when you post answers in the future. And welcome to Physics Stack Exchange! – David Z Nov 26 '12 at 18:16

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.