Consider a particle on a ring that is perturbed by interacting with an applied electric field (E) with the perturbation being H' = μE cos Φ, where μ is the dipole moment. The energy levels correct upto first order are

Concept:

• Perturbation theory is an approximation method to find out the exact solution of any system with great accuracy.
• To break the energy correction in a particular energy level, we have to disturb the operator in a specific order.
• The energy correction is given by,

• The perturbed energy levels upto first order are given by,

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• For a particle in a ring, the ground state quantized energy values are,

, where ml is the magnetic quantum number.

Explanation:

• For a particle in a ring that is perturbed by interacting with an applied electric field (E) with the perturbation being

• For a particle in a ring, the wavefunction is given by,

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• The first-order perturbed energy () is given by,

=0

Conclusion:

• Hence, energy levels correct upto first order are,

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