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    ​A perturbation​is applied to a rigid rotator undergoing a rotational motion in a plane. The first order energy correction to the ground state is
    Question

    ​A perturbation

    ​is applied to a rigid rotator undergoing a rotational motion in a plane. The first order energy correction to the ground state is

    A.

    B.

    C.

    D.

    Correct option is C

    Time-independent perturbation theory

    In perturbation theory, we suppose that the Hamiltonian for the problem we are trying to solve,

    can be expressed as the sum of a simple Hamiltonian,

    which has known eigenvalues and eigenfunctions, and a contribution,

    which represents the extent to which the true Hamiltonian differs from the ‘model’ Hamiltonian:

    ​In time-independent perturbation theory, the perturbation is always present and unvarying. For example, it might represent a dip in the potential energy of a particle in a box in some region along the length of the box. In time-independent perturbation theory, we suppose that the true energy of the system differs from the energy of the simple system, and that we can write

    The first-order corrections to the energy of the ground state 

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