Hi, 5.27 problem in liboff says that if [itex] g(A)f(\varphi) = g(a)f(\varphi),where A\varphi = a\varphi [/itex](adsbygoogle = window.adsbygoogle || []).push({});

I tried to solve this problem with tylar expansion.

[itex] f(\varphi) = f(0) + f^{'}(0)\varphi + \frac{f^{''}(0)}{2!}\varphi^2 + \frac{f^{(3)}(0)}{3!}\varphi^3 + ...[/itex]

[itex] g(A) = g(0) + g^{'}(0)A + \frac{g^{''}(0)}{2!}A^2 + \frac{g^{(3)}(0)}{3!}A^3 + ...[/itex]

But when i applied g(A) to f([itex]\varphi[/itex]) i can not get right hand side of equality

written above because i don't know how can i deal with unseen term such as

[itex] A\varphi^2 [/itex]or [itex]A^2\varphi [/itex] or etc

please assist to me.

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# [Q]Analytic function of operator A

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