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1. For an one-dimensional harmonic oscillator, the Hamiltonian is given as p2 +kx?. 1 H 2m (1a) Derive the Hamiltonian equation of motion. (1b) For the Hamiltonian given in Problem- derive the expression for the Lagrangian and the Lagrangian equation of motion. (1c) Verify if energy is conserved for the Hamiltonian given in Problem

1. For an one-dimensional harmonic oscillator, the Hamiltonian is given as p2 +kx?. 1 H 2m (1a) Derive the Hamiltonian equation of motion. (1b) For the Hamiltonian given in Problem- derive the expression for the Lagrangian and the Lagrangian equation of motion. (1c) Verify if energy is conserved for the Hamiltonian given in Problem

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1. For an one-dimensional harmonic oscillator, the Hamiltonian is given as p² +kx². H = 2m 2 (1a) Derive the Hamiltonian equation of motion. (1b) For the Hamiltonian given in Problem- derive the expression for the Lagrangian and the Lagrangian equation of motion. (1c) Verify if energy is conserved for the Hamiltonian given in Problem
Transcribed Image Text:1. For an one-dimensional harmonic oscillator, the Hamiltonian is given as p² +kx². H = 2m 2 (1a) Derive the Hamiltonian equation of motion. (1b) For the Hamiltonian given in Problem- derive the expression for the Lagrangian and the Lagrangian equation of motion. (1c) Verify if energy is conserved for the Hamiltonian given in Problem
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