The very first thing my textbook says is that the Hamilton operator is defined as: $$\vec{\nabla}=\vec{a}^i\nabla_i$$ Where $\nabla_i$ is the covariant derivative and " $\vec{a}^i$ is the curvilinear basis of the curvilinear coordinates $\xi ^i$". However I can't understand if that should be the dual basis (because of the upper index) or it is just written that way to obey einstein notation (upper and lower repeating) or maybe it is a mistake (I don't believe it to be). Can you help me clarify this? In case you are wondering for the textbook, It's called "Лекции по векторно и тензорно смятан�� за физици" in Bulgarian and the question I'm asking is regarding the content on 57-th page. Here's the pdf: "drive.google.com/file/d/1snb8EGaFl96w1-Ti7c17ib2ICyhtjG1U/view"
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