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The Hamiltonian of a relativistic particle of rest mass m and momentum p is given by 
in units in which the speed of light c = 1. The corresponding Lagrangian is:
in units in which the speed of light c = 1. The corresponding Lagrangian is:- a)
- b)
- c)
- d)
Correct answer is option 'A'. Can you explain this answer?
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The Hamiltonian of a relativistic particle of rest mass mand momentum ...
Here, the Hamiltonian of relativistic particle is given as,
Where, p is momentum and m is the mass.
Now, as we know that Lagrangian transformation is given as,
Where, q is the position co-ordinate of the particle. Here is our case q= x, therefore equation (2) can be written as,
Now, from Hamilton's equation,
Substitute the value of equation (4) in equation (3).
Where, p is momentum and m is the mass.
Now, as we know that Lagrangian transformation is given as,
Where, q is the position co-ordinate of the particle. Here is our case q= x, therefore equation (2) can be written as,
Now, from Hamilton's equation,
Substitute the value of equation (4) in equation (3).
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The Hamiltonian of a relativistic particle of rest mass mand momentum pis given byin units in which the speed of light c = 1.The corresponding Lagrangian is:a)b)c)d)Correct answer is option 'A'. Can you explain this answer?
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