# QUOTIENT OF TWO OPERATORS

• wasi-uz-zaman
In summary, the conversation discusses the notation for A/B, which can be read either as AB^-1 or B^-1A. The reason for this ambiguity is that A/B is typically read left to right, leading to the notation AB^-1. However, this notation may not be clear for non-commutative objects. The conversation also mentions that the notation may not be used in some languages, such as Arabic and Japanese, due to different reading directions.

#### 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

wasi-uz-zaman said:
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.

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

Thanks
Bill

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

Nugatory
wasi-uz-zaman said:
HI, Suppose there are two operators A and B , We have to find A /B
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.

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?

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

naima said:
I think that arab physicists will not be convinced by this answer!
how do you know i am arab

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

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

wasi-uz-zaman said:
how do you know i am arab

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.

bhobba
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.