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Physics / Classical Mechanics 0 / Chapter 4 / Problem 4.50

Classical Mechanics | 0th Edition | ISBN: 9781891389221 | Authors: John R Taylor

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The formalism of the potential energy of two particles

Chapter 4, Problem 4.50

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QUESTION:

The formalism of the potential energy of two particles depends on the claim in (4.81) that V1U(r1 r2) = V2U(r1 r2). Prove this. (Use the chain rule for differentiation. The proof in three dimensions is notationally awkward, so prove the one-dimensional result that a a ax f (xi x2) = f (xi x2) , ax2 and then convince yourself that it extends to three dimensions.)

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QUESTION:

The formalism of the potential energy of two particles depends on the claim in (4.81) that V1U(r1 r2) = V2U(r1 r2). Prove this. (Use the chain rule for differentiation. The proof in three dimensions is notationally awkward, so prove the one-dimensional result that a a ax f (xi x2) = f (xi x2) , ax2 and then convince yourself that it extends to three dimensions.)

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