Finding the factor by which two operators differ.

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SUMMARY

The discussion centers on the mathematical comparison of two operators, specifically A^2B^2 + B^2A^2 and 1/2(A^B^+B^A^)². The participant expresses confusion regarding the phrasing of the question, suggesting it should inquire about the factor by which two operations differ instead of operators. The participant contemplates using inner products or commutation to find the relationship between the two operators but seeks clarity on the question's intent rather than direct mathematical assistance.

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1. Homework Statement
I have two operators
A^2B^2+B^2A^2

1/2(A^B^+B^A^) 2

By what factor do the two operators differ?


3. The Attempt at a Solution
I believe I either have to find the inner products of them and relate them somehow or use commutation?
Not sure which one!
I don't want help with the maths as I really need to try figure that bit out myself! But I am not quite sure what the question is asking me to do.
 
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Shouldn't the question read "By what factor do the two operations differ"?
That is the result of the two operations differ by only a factor, or one answer is a factor of the other.
 
Thats not how the question is worded :/ Would maybe make more sense like that...But it definitely says by what factor do the two operators given differ.
 
That doesn't make sense. Operators are defined a certain way and give variable results when operating on the operands. So I would think they intended to write 'operations'. If that is what they really intended why would they give two equations then?
 

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