Finding the Ground State Energy for Bosons and Fermions.
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Consider three particles, each of mass m, moving in one dimension and bound to eachother by harmonic forces, i.e., V=k/2*[(x_1-x_2)^2+(x_2-x_3)^2+(x_3-x_1)^2]
1) Write the (time-independent) schrodinger equation for the system.
2) Transform to a new coordinate system (having the center of mass as one of the coordinates), so that one can readily solve for the energy eigenvalues and the corresponding eigenfunctions explicitly.
3) Using the result of 2), find the ground state energy if the particles are identical spin-0 bosons.
4) What is the ground state energy if the particles are identical spin-1/2 fermions?
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Solution Summary
The response solves the Schrodinger equation for a system of three coupled particles and compute the ground state energy of the system in the cases in which the particles are bosons or fermions. Contains a Word attachment.
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We are given three particles, each of mass m, moving in one dimension and bound to each other by harmonic forces given by the following potential:
1. We wish to write down the time-independent Schrodinger equation for this system.
We have
2. We wish to transform to a new coordinate system so that the Schrodinger equation can be solved explicitly in terms ...
Purchase this Solution
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