Fermions & bosons in a 1D infinite well

Simulation

Challenges

Spatial wave function

ψspace(x1, x2) = ɸ1(x1) ɸ2(x2)

No symmetry under exchange x1x2

0L/20L/2
x2x1

Spatial wave function ψspace

Indistinguishable particles with spin

Consider two non-interacting quantum particles in the same one-dimensional infinite square well. You can change the particle energies and the types of particles displayed. The contour graphs show maxima in red and minima in blue. What does it mean graphically to
exchange the two particles, and how do the ψspace and |ψspace|2 graphs behave under particle exchange for the various configurations? Then go on to the Challenges!

Energy controls

Esystem = 1E1 + 4E1 = 5E1

energy levels in the 1D infinite well

E1

E2 = 4E1

E3 = 9E1

E4 = 16E1

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