α I have been studying translation operators of the type T = exp ( -ipx(adsbygoogle = window.adsbygoogle || []).push({}); _{0}/ hbar) where p is the momentum operator which leads to T^{+}xT = x+x_{0}. I am ok with that but then I came across the following equation concerning raising and lowering operators exp(-alpha a^{+}) a exp(alpha a^{+}) = a + alpha. Is this equation related to the translation operator or is it something different ?

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# Translation operators

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