hw2 - HOMEWORK ASSIGNMENT 2 PHYS852 Quantum Mechanics I,...

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Unformatted text preview: HOMEWORK ASSIGNMENT 2 PHYS852 Quantum Mechanics I, Spring 2008 Topics covered: 1st order perturbation theory 1. The two-level Rabi model is ubiquitous in quantum mechanics. In order to compare the results of perturbation theory with the exact results, find the exact eigenvalues and eigenstates of the Hamil- tonian H = S z + S x . Use as your basis states: | ) for spin up and | ) for spin down, relative to the z-axis. Compare your answer to the results from first-order perturbation theory derived in class. 2. The relative motion of two identical particles in a harmonic potential is described by the Hamiltonian H = P 2 2 + 1 2 X 2 , where X and P are in dimensionless units. If the particles are spin-polarized (i.e. same spin ori- entation) bosons, then symmetry requires that only the even energy levels be allowed, while if the particles are spin-polarized fermions then only the odd levels are allowed. Consider the effect of an inter-particle contact interaction V = g ( X ). To first-order in perturbation theory compute the)....
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This note was uploaded on 11/26/2010 for the course PHYSICS PHYS 852 taught by Professor Michaelmoore during the Spring '10 term at Michigan State University.

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