Explore BrainMass

# Multiparticle Schrodinger Equation

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

Please help with the following problem.

Two identical spin-1/2 particles with mass m are in a one-dimensional infinite square-well potential with width a, so V(x)=0 for 0 <= x <= a, and there are infinite potential barriers at x=0 and x=a. The particles do not interact with each other; they see only the infinite square-well potential.

a) Calculate the energies of the three lowest-energy singlet states.
b) Calculate the energies of the three lowest-energy triplet states.
c) Suppose that the particles are in a state with wave function

psi(x_1, x_2) = (1/sqrt(2))(2/a)(sin((pi)x_1/a)sin(7(pi)x_2/a) +
+sin((pi)x_2/a)sin(7(pi)x_1/a))

where x_1 is the position of particle 1 and x_2 is the position of particle 2. Are the particles in a triplet spin state or a singlet spin state? Explain.

© BrainMass Inc. brainmass.com June 4, 2020, 12:22 am ad1c9bdddf
https://brainmass.com/physics/energy/multiparticle-schrodinger-equation-335106

#### Solution Preview

Hello and thank you for posting your question to Brainmass!

The solution is attached below ...

#### Solution Summary

This solution helps with a problem involving the multiparticle Schrodinger equation. Step by step calculations are given.

\$2.19