The effective one-body Hamiltonian for a single particle in a central well can be written in spherical coordinates as 1 H(p, q) = 2/1/12 ( P² + 1/2 (P² + ₁ in ² 0 P ²)) + 2m r2 sin² 3)) + V (7) V(r) Derive the Hamilton's equations of motion and prove that (p² + p² / sin² 0) = £² is a constant of motion.
The effective one-body Hamiltonian for a single particle in a central well can be written in spherical coordinates as 1 H(p, q) = 2/1/12 ( P² + 1/2 (P² + ₁ in ² 0 P ²)) + 2m r2 sin² 3)) + V (7) V(r) Derive the Hamilton's equations of motion and prove that (p² + p² / sin² 0) = £² is a constant of motion.
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Transcribed Image Text: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 / 2 (P ² + 1 -/- (P² + si ²2 0 P ₁ ) ) + V (r)
Pa
2m
sin²
Derive the Hamilton's equations of motion and prove that (p² + p² / sin² 0) = £² is a
constant of motion.
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