Consider three non-interacting electrons confined to a one-dimensional infinite potential well of width a, where V(x)...

  

Transcribed Image Text:

Consider three non-interacting electrons confined to a one-dimensional infinite potential well of width a, where V(x) = 0 for 0 x a and V(x) = otherwise. The single particle eigenfunctions including the spatial wavefunction and spin state are 2 nx = n -sin(- *)([1], [0]), & -= 2 nX = sin()([0],[1]) a n a a a (a) [5 marks] Find the ground state energy and argue that the degeneracy is two. (b) [5 marks] Write down the ground state wavefunctions. (c) [5 marks] What is the total spin S of the ground state? (d) [10 marks] Now instead assume you have three bosons (without spin) in the same potential well. What is the ground state energy, the degeneracy, and the ground state wavefunction(s)? Consider three non-interacting electrons confined to a one-dimensional infinite potential well of width a, where V(x) = 0 for 0 x a and V(x) = otherwise. The single particle eigenfunctions including the spatial wavefunction and spin state are 2 nx = n -sin(- *)([1], [0]), & -= 2 nX = sin()([0],[1]) a n a a a (a) [5 marks] Find the ground state energy and argue that the degeneracy is two. (b) [5 marks] Write down the ground state wavefunctions. (c) [5 marks] What is the total spin S of the ground state? (d) [10 marks] Now instead assume you have three bosons (without spin) in the same potential well. What is the ground state energy, the degeneracy, and the ground state wavefunction(s)?