# Power series method help

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#1
I would like to get only the first order terms in h-bar, but I am not sure how to go about this...
I used j=0 for the first term, but since j can only be an integer, (based on the physical situation) I'm not sure what to do about the second term. Help!
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3 weeks ago
#2
(Original post by IDontKnowReally)
I would like to get only the first order terms in h-bar, but I am not sure how to go about this...
I used j=0 for the first term, but since j can only be an integer, (based on the physical situation) I'm not sure what to do about the second term. Help!
When you say 'first order terms', which variable's order are you referring to? Is it h?
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#3
Yes, h sorry, not h-bar!
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3 weeks ago
#4
(Original post by IDontKnowReally)
Yes, h sorry, not h-bar!

At order we have;

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#5
(Original post by RDKGames)

At order we have;

Yes, I got the same for the zero-th order, but for the first order, how do you get this term:
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3 weeks ago
#6
(Original post by IDontKnowReally)
Yes, I got the same for the zero-th order, but for the first order, how do you get this term:
It's because of the squaring.

You are multiplying two brackets;

The overall coefficient of h term will come in when we either:

-- Take from first bracket and multiply it by in second bracket.
-- Take from first bracket and multiply it by in second bracket.

Thus, this squared sum at order h is simply i.e.
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#7
(Original post by RDKGames)
It's because of the squaring.

You are multiplying two brackets;

The overall coefficient of h term will come in when we either:

-- Take from first bracket and multiply it by in second bracket.
-- Take from first bracket and multiply it by in second bracket.

Thus, this squared sum at order h is simply i.e.
Ohhh, that makes so much more sense thanks! I kept thinking of the second sum as being which confused me.
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3 weeks ago
#8
(Original post by IDontKnowReally)
Ohhh, that makes so much more sense thanks! I kept thinking of the second sum as being which confused me.
Oh no, rookie error!

otherwise we would say !
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