Occupation numbers & quantum statistics University Advanced Quantum Mechanics · Second quantisation
Exchange Lock
Pack bosons or fermions into one-particle states to meet a particle-count and energy lock.
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Challenge 1 of 3
Bosons may share a state
Place three noninteracting bosons in four labelled one-particle states.
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Use exactly 3 particles and make the total energy 1.9–2.1 eV.
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Construct number states, enforce Pauli exclusion for fermionic one-particle states, and calculate the energy of noninteracting occupations.
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The physics behind the game
Construct number states, enforce Pauli exclusion for fermionic one-particle states, and calculate the energy of noninteracting occupations.
N = Σnᵢ; E = Σεᵢnᵢ; fermions nᵢ ∈ {0,1}; bosons nᵢ = 0,1,2,…
Model assumptions. Four distinct orthonormal one-particle states, each already including its spin label where needed. Two fermions cannot occupy the same complete one-particle state; two opposite-spin states may share a spatial orbital. Particles are noninteracting, so energies add. Fermion exchange signs are not visualised by this number-state puzzle.