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Unformatted text preview: p i = L / x i . Show that if L = T V , and T = i j T ij x i x j , where the T ij s are constants, then H = T + V . You may assume with no loss of generality that T ij = T ji . 1 6. Shankar, problem 2.7.2 (i). 7. OPTIONAL; NOT TO BE TURNED IN: Suppose we have a particle in one dimension, whose Lagrangian is L = mc 2 r 1 x 2 /c 2 V ( x ) , (2) where m and c are positive constants. (Actually, m is the rest mass and c is the speed of light.) Assume | x | < c . (a). Find the Lagrange equation of motion for this particle. (b). Find the canonical momentum p = L / x . (c). Find the corresponding Hamiltonian H . (d). What is H in the limit | x | c ? 2...
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