# QUOTIENT OF TWO OPERATORS

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1. Feb 5, 2015

### wasi-uz-zaman

HI, Suppose there are two operators A and B , We have to find A /B - Will it equal to AB-1
OR B-1 A , Because i have read that it equals to AB-1 , BUT i could not find reason for that.
thanks

2. Feb 5, 2015

### bhobba

There is no reason - its just A/B is read left to right so you tend to write it as AB^-1.

Thanks
Bill

3. Feb 5, 2015

### naima

I think that arab physicists will not be convinced by this answer!

4. Feb 5, 2015

### kith

Who asks you this? I have never seen this notation and I think it isn't used precisely because it is ambiguous.

Generally in abstract algebra, $\frac{x}{y}$ is a shorthand notation for $xy^{-1}$ in the case that the algebraic structure is commutative. If the structure is not commutative, it simply isn't used.

5. Feb 5, 2015

### cgk

I'd like to second kith's opinion. Do not use $\frac{x}{y}$ unless you are dealing with commutative objects. At best, it would be confusing, in other cases, it would be simply wrong. Note, for example,that $xy^{-1}$ and $y^{-1}x$ are not even the only things this could possibly mean. Who says it should not be $y^{-1/2}xy^{-1/2}$ or something entirely different?

6. Feb 7, 2015

### wasi-uz-zaman

hello , i have read this in BOOK " QUANTUM MECHANICS CONCEPT AND APPLICATION" (SECOND EDITION) BY Zettili , on problem 2.12 on page 147.

7. Feb 7, 2015

### wasi-uz-zaman

how do you know i am arab

8. Feb 7, 2015

### wasi-uz-zaman

hello i have read this in book " quantum mechanics concepts and applicatiotion" by zettlii page 147 2nd edition

9. Feb 7, 2015

### Staff: Mentor

He doesn't. Naima was pointing out that Bhobba's answer wouldn't be particularly helpful to someone whose native language is written right-to-left, and Arabic is the first example that came to mind.

10. Feb 7, 2015

### naima

You are right.
Israeli also write from right to left and up to down.
It becomes more complicated with traditional japonese.
Things can be read from up to down and then from right to left so $\frac {x}{y}$ has no asymmetry.