Finding the factor by which two operators differ.

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The discussion revolves around understanding the difference between two operators, A^2B^2 + B^2A^2 and 1/2(A^B^+B^A^). The original question asks by what factor the two operators differ, but there is confusion regarding the wording, suggesting it should refer to "operations" instead. The participant is uncertain whether to use inner products or commutation to find the relationship between the operators. They emphasize the importance of grappling with the mathematical aspects independently while seeking clarity on the question's intent. Ultimately, the distinction between operators and operations is central to resolving the confusion.
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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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