The Lagrangian of a particle of charge e and mass in in applied electric and magnetic fields is given by L =m + eAV - cộ, where a and o are the vector and scalar potentials corresponding to the magnetic and electric fields, respectively. Which of the following statements is corecet? (a) The canonically conjugate momentum ofthe particle is given by p = mv 92. (NET June 2011] (b) The Hamiltonian of the particle is given by H . 2m m ()L remains unchanged under a gange transformation ofthe potentials (d) Under a gauge transformation of the potentials, L changes by the total time derivitive of function of andt
The Lagrangian of a particle of charge e and mass in in applied electric and magnetic fields is given by L =m + eAV - cộ, where a and o are the vector and scalar potentials corresponding to the magnetic and electric fields, respectively. Which of the following statements is corecet? (a) The canonically conjugate momentum ofthe particle is given by p = mv 92. (NET June 2011] (b) The Hamiltonian of the particle is given by H . 2m m ()L remains unchanged under a gange transformation ofthe potentials (d) Under a gauge transformation of the potentials, L changes by the total time derivitive of function of andt
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![The Lagrangian of a particle of charge e and mass in in applied electric and magnetic
fields is given by L=m + eAv- eộ, where z and o are the vector and scalar
potentials corresponding to the magnetic and electric fields, respectively. Which of the
92.
following statements is correct?
(NET June 2011]
(a) The canonicallyconjugate momentum ofthe particle is given by p = mỹ
(b) The Hamitonian ofthe particle is given by H
2m m
(e)L remains unchanged under a gange transformation of the potentials
(d) Under a gauge transformation of the potentials, Lchanges by the total time derivitive
of function of andt](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F303465d4-194d-4c7f-a0d2-2e88266cd0f7%2Ff1df2f5a-3c05-4469-89ad-cb2c131d02c0%2Fum092d6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The Lagrangian of a particle of charge e and mass in in applied electric and magnetic
fields is given by L=m + eAv- eộ, where z and o are the vector and scalar
potentials corresponding to the magnetic and electric fields, respectively. Which of the
92.
following statements is correct?
(NET June 2011]
(a) The canonicallyconjugate momentum ofthe particle is given by p = mỹ
(b) The Hamitonian ofthe particle is given by H
2m m
(e)L remains unchanged under a gange transformation of the potentials
(d) Under a gauge transformation of the potentials, Lchanges by the total time derivitive
of function of andt
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