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For a non-relativistic particle of mass m and charge q in an electromagnetic field, the Lagrangian...

For a non-relativistic particle of mass m and charge q in an electromagnetic field, the Lagrangian function is given by L = (m /2) v · v − q(φ − v · A). Show that the Hamiltonian can be written as H = (1 /2) (p − qA) · (p − qA) + qφ, where p is the canonical momentum.For a non-relativistic particle of mass m and charge q in an electromagnetic field, the Lagrangian function is given by L =( m/ 2) v · v − q(φ − v · A). Show that the Hamiltonian can be written as H =( 1 /2 )(p − qA) · (p − qA) + qφ, where p is the canonical momentum.

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