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I do not know how to find that. I've found two separate solutions, both of which write the potential, wave hands, and promptly write the answer. The link above says "Here we simply need to Taylor expand the expression in (1)." I can do a simple Taylor expansion, so I have an idea what it looks like, but I have no clue what it has to do with this problem. The author's next two equations are just (1) multiplied out, with some jabber inbetween I can't make heads or tails of. Then they write the answer.

Could anyone help me along in how this answer is found? I have actually spent a great deal of time trying to figure out how this is solved, but I cannot seem to get the solution.

Thanks.