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Instead we choose [itex]1/2(\underline{x}[/itex].[itex]\underline{p}/r+\underline{p}[/itex].[itex]\underline{x}/r)[/itex].

If it is because the former expression is not Hermitian (which is what I think), can someone help me prove it? If it is something else, then may I know why we choose this strange "averaged" expression?

Thank you.