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I have been looking at the solutions to a past exam question. The question gives the annihilation operator for the harmonic oscillator as a= x + ip ( I have left out the constants ). The question then asks to calculate the Hermitian conjugate a(dagger).

I thought to find the Hermitian conjugate I just change the sign of the imaginary component and this does give the right answer and most books just state this as the conjugate but the exam solution goes on to use inner products and integration by parts. I'm confused !

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# Hermitian conjugate of the annihilation operator

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