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The relativistic Lagrangian for a particle of rest mass m moving along the x-axis in a potential V(x) is given by √√₁-222-V(a) L = mc² [Expect to use a few lines to answer these questions.] a) Derive the Euler-Lagrange equation of motion. b) Show that it reduces to Newton's equation in the limit |ż| << c. c) Compute the Hamiltonian of the system.

The relativistic Lagrangian for a particle of rest mass m moving along the x-axis in a potential V(x) is given by √√₁-222-V(a) L = mc² [Expect to use a few lines to answer these questions.] a) Derive the Euler-Lagrange equation of motion. b) Show that it reduces to Newton's equation in the limit |ż| << c. c) Compute the Hamiltonian of the system.

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The relativistic Lagrangian for a particle of rest mass m moving along the x-axis in a potential V(x) is given by ²√₁-22-1 V(x) L = -mc² √ [Expect to use a few lines to answer these questions.] a) Derive the Euler-Lagrange equation of motion. b) Show that it reduces to Newton's equation in the limit |ż| < c. c) Compute the Hamiltonian of the system.
Transcribed Image Text:The relativistic Lagrangian for a particle of rest mass m moving along the x-axis in a potential V(x) is given by ²√₁-22-1 V(x) L = -mc² √ [Expect to use a few lines to answer these questions.] a) Derive the Euler-Lagrange equation of motion. b) Show that it reduces to Newton's equation in the limit |ż| < c. c) Compute the Hamiltonian of the system.
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