Aid for understanding some calculations

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The discussion centers on understanding the calculations presented in Equation 50 on page 14 of the paper available at arXiv:quant-ph/0108132v1. The primary focus is on expanding the operator ##\hat U## as a Taylor series. The user expresses difficulty in performing these calculations without matrix representations and seeks clarification on the abstract methodology involved, rather than specific numerical solutions.

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ShayanJ
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Its a while I'm trying to understand [ http://arxiv.org/pdf/quant-ph/0108132v1.pdf ] but i have problem following its calculations.The part I have problem in now is the expansion in page 14,Eq. 50.Can anyone help me understand how that is done?
Thanks
 
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Shyan said:
Its a while I'm trying to understand [ http://arxiv.org/pdf/quant-ph/0108132v1.pdf ] but i have problem following its calculations.The part I have problem in now is the expansion in page 14,Eq. 50.Can anyone help me understand how that is done?
Thanks
Expand ##\hat U## as a Taylor series.

(If you need any more help than that, then please show your work, as if this were a question in the homework forum.)
 
strangerep said:
Expand ##\hat U## as a Taylor series.

(If you need any more help than that, then please show your work, as if this were a question in the homework forum.)

I know that.The point is,I don't know how to do such calculations in this abstract manner and without using matrix representations and with that method,I don't seem to get the same result as that of the mentioned paper.
So,this is not actually like a homework thread,because i don't want the exact calculations.I just want an explanation,with some little examples,to understand how should I do it because I can't find a reference which helps me to understand that.
Still,if it seems a homework thread to you,I should say I don't know what to do from the first place,so I can show no work!
 

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