sp03mod - PHY6938 Proficieny Exam Spring 2003 Modern...

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PHY6938 Proficieny Exam Spring 2003 March 28, 2003 Modern Physics and Quantum Mechanics 1. Light of wavelength 300 nm strikes a metal plate, producing photoelectrons that move with speed of 0 . 002 c . (a) What is the work function of the metal ? (b) What is the critical wavelength for this metal, so that photoelectrons are pro- duced ? (c) What is the significance of the critical wavelength ? 2. A system consists of two distinguishable particles of mass m, bound in an infinite- strength one-dimensional square well potential of width a . They have no spin and do not interact. The one-particle states are given by Ψ n ( x ) = s 2 a sin a x (a) Write the 2-body Hamiltonian in terms of the individual particle coordinates x 1 and x 2 . Write down the wave-functions for all excited states. (b) Verify that they are eigenfunctions of the Hamiltonian and find their energy. (c) Consider now that both particles are identical bosons. Write down the excited state wave-functions. What changes with respect to part (b) ? You may ignore the normalization of the wavefunction.
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