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3. The effective one-body Hamiltonian for a single particle in a central well can be written in spherical coordinates as 1 1 H(p.q) = 2m (P² + 1 (P² + m ² @ P³)) + V(r) sin²0 Derive the Hamilton's equations of motion and prove that (p² + p²/sin² 0) = ² is a constant of motion.

3. The effective one-body Hamiltonian for a single particle in a central well can be written in spherical coordinates as 1 1 H(p.q) = 2m (P² + 1 (P² + m ² @ P³)) + V(r) sin²0 Derive the Hamilton's equations of motion and prove that (p² + p²/sin² 0) = ² is a constant of motion.

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3. The effective one-body Hamiltonian for a single particle in a central well can be written in spherical coordinates as 1 1 1 H (p, q) = = 2 m ( P² + = 2 (P² + ₁in² P²)) + V(r) 2m 0 Derive the Hamilton's equations of motion and prove that (p² + p² / sin² 0) = £² is a constant of motion.
Transcribed Image Text:3. The effective one-body Hamiltonian for a single particle in a central well can be written in spherical coordinates as 1 1 1 H (p, q) = = 2 m ( P² + = 2 (P² + ₁in² P²)) + V(r) 2m 0 Derive the Hamilton's equations of motion and prove that (p² + p² / sin² 0) = £² is a constant of motion.
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