1. Planar rotator is a one-degree of freedom physical system that can execute rotational motion in...

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1. Planar rotator is a one-degree of freedom physical system that can execute rotational motion in a plane. Its classical Hamiltonian function is H = M 21 (1) where M, is the projection of the angular momentum vector onto the z-axis that is perpendicular to the plane of rotation and I is the moment of inertia of the system about the z-axis. The Hamiltonian operator of the planar rotator has the form where 21 21 d is the rotation angle about the z-axis. (a) Give at least 3 examples of planar rotators. (b) What physical quantities are conserved for the planar rotator? (c) What are the normalized eigenfunctions and eigenvalues of the operator [? (2) (d) Determine the stationary state wave functions and energy levels of the planar rotator. How is this question related to your answers in part (c)? (e) What is the degeneracy of the energy levels? 1. Planar rotator is a one-degree of freedom physical system that can execute rotational motion in a plane. Its classical Hamiltonian function is H = M 21 (1) where M, is the projection of the angular momentum vector onto the z-axis that is perpendicular to the plane of rotation and I is the moment of inertia of the system about the z-axis. The Hamiltonian operator of the planar rotator has the form where 21 21 d is the rotation angle about the z-axis. (a) Give at least 3 examples of planar rotators. (b) What physical quantities are conserved for the planar rotator? (c) What are the normalized eigenfunctions and eigenvalues of the operator [? (2) (d) Determine the stationary state wave functions and energy levels of the planar rotator. How is this question related to your answers in part (c)? (e) What is the degeneracy of the energy levels?