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# Discussion10 - Physics 486 Fall 2007 Discussion Problems 10...

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Physics 486 Fall 2007 Discussion Problems 10 1). Two masses, m 1 and m 2 , which are restricted to moving in a plane, are connected by a massless rod of length R to form a rigid rotator. Notes: one can turn this into a one particle problem by using a reduced mass μ =m 1 m 2 /(m 1 +m 2 ). Also, this system has only 1 degree of freedom, which can be chosen to be either the arc length S or the rotational angle ϕ , where S=R ϕ . (a) Write down the Schrödinger equation for this system. (b) Determine the unnormalized eigenstates of the SEQ in part (a). (c) By imposing the requirement that the wavefunction must be single-valued, determine the energy eigenvalues for the rigid rotator: (d) Show that the eigenstates of the Hamiltonian, which you determined in (b), are also eigenstates of the angular momentum operator L z . What does this tell you about the operators H and L z ? Verify that H and L z commute. What are the measurable values of the angular momentum for this system?

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Discussion10 - Physics 486 Fall 2007 Discussion Problems 10...

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