hw5_002 - PHY 4604 Fall 2009 Homework 5 Due at the start of...

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PHY 4604 Fall 2009 – Homework 5 Due at the start of class on Monday, November 2. No credit will be available for homework submitted after the start of class on Friday, November 6. Answer both questions. Please write neatly and include your name on the front page of your answers. You must also clearly identify all your collaborators on this assignment. To gain maximum credit you should explain your reasoning and show all working. You may find useful tanh x = 1 coth x = e x - e - x e x + e - x ( x for | x 1 sgn x for | x 1 . 1. As a greatly simplified model of a diatomic molecule, consider a particle of mass m moving in the one-dimensional potential V ( x )= - v ~ 2 2 ma h δ ± x - a 2 ² + δ ± x + a 2 ²i , where a> 0 is the bond length (i.e., the distance between the two nuclei), and v> 0isa dimensionless real number that parametrizes the strength of the short-range attractive potential centered on each nucleus. This question concerns possible bound states of this potential, i.e., stationary states having energies E = - ~ 2 K 2 / 2 m< 0. Since V ( - x )= V ( x ), any such bound state can be classified as being even or odd under x →- x . (a) Write down the general form of an even bound-state wave function. Apply the appropriate boundary conditions to obtain an equation relating Ka and v ,wh ich
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This note was uploaded on 12/15/2011 for the course PHY 4604 taught by Professor Field during the Fall '07 term at University of Florida.

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hw5_002 - PHY 4604 Fall 2009 Homework 5 Due at the start of...

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