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This very much depends on what you want to do in the area of quantum theory. If you want to solve specific mathematical problems and to have only a very rough conception of why you are doing what you are doing, then you can in principle omit classical mechanics. But if you want to have a well-rounded knowledge of the subject, you should know some basics of ...

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Both ways are possible. Since you seem to be a mathematician, let me try an analogy from mathematics. Say that you are accomplished in commutative algebra. Now, you want to study algebraic geometry. Sure, you can start with sheaves of local rings and cohomology of schemes, instead of "at the bottom" with classical algebraic varieties defined by polynomial ...

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Historically, one motivating experiment for kinetic energy was dropping balls into clay and noting the relation between impact speed $v$ and the impact depth $d$: $$v^2 \propto d$$ I suspect this experiment could be modified to show the role that mass plays and obtain $d\propto mv^2$. A different experiment would be to launch a cart using some type of ...

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