Answer to Question #155785 in Quantum Mechanics for Asad

Question

A particle of mass mis fixed at one end of a rigid rod of negligible mass and length R The other end of the rod rotates in the xy plane about a bearing located at the origin, whose axis is in the z-direction. (a) Write the system's total energy in terms of its angular momentum L. (b) Write down the time-independent Schrödinger equation of the system Calculate the energy eigenvalues of an axially symmetric rotator and find the degeneracy of each energy level (i.c., for each value of the azimuthal quantum number m, find how many states (1. m) correspond to the same energy). We may recall that the Hamiltonian of an axially symmetric rotator is given by 2+2; 21: where and I2 are the moments of inertia. (b) From part (a) infer the energy eigenvalues for the various levels of I = 3. (c) In the case of a rigid rotator (ie, h = h = 1), find the energy expression and the corresponding degeneracy relation (d) Calculate the orbital quantum number and the corresponding energy degeneracy for a rigid rotator where the magnitude of the total angular momentum is 561.

Answer 1

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