Q1. A particle of mass m is moving in a central potential V that does not depend on velocity. Set up Hamiltonian and try different quantities Poisson bracket with the Hamiltonian to find if they are constants (integrals) of motion. Solve (i) [pr, H] (ii) [po, H] (iii) [p3, H] 2 (iv) [p} + P‚H]
Q1. A particle of mass m is moving in a central potential V that does not depend on velocity. Set up Hamiltonian and try different quantities Poisson bracket with the Hamiltonian to find if they are constants (integrals) of motion. Solve (i) [pr, H] (ii) [po, H] (iii) [p3, H] 2 (iv) [p} + P‚H]
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![Q1. A particle of mass m is moving in a central potential V that
does not depend on velocity. Set up Hamiltonian and try different
quantities Poisson bracket with the Hamiltonian to find if they are
constants (integrals) of motion.
Solve
(i) [pr, H]
(ii) [po, H]
(iii) [p3, H]
(iv) [p² +
P²
sin² 0
)
H]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6c9f9b7f-9cdb-48f2-b60f-7a0f50ac2664%2Ffdf93292-0c24-42fe-a5fa-3a5f25052b63%2F2ox0y_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Q1. A particle of mass m is moving in a central potential V that
does not depend on velocity. Set up Hamiltonian and try different
quantities Poisson bracket with the Hamiltonian to find if they are
constants (integrals) of motion.
Solve
(i) [pr, H]
(ii) [po, H]
(iii) [p3, H]
(iv) [p² +
P²
sin² 0
)
H]
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