Problem 4. Consider two indistinguishable, noninteracting spin-1/2 fermions in a one- dimensional infinite square well potential of length L. (a) What is the ground-state energy of the two-particle system? (b) What is the ground-state quantum state vector? (c) What is the first excited state energy of the two-particle system?

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Problem 4. Consider two indistinguishable, noninteracting spin-1/2 fermions in a one-
dimensional infinite square well potential of length L.
(a) What is the ground-state energy of the two-particle system?
(b) What is the ground-state quantum state vector?
(c) What is the first excited state energy of the two-particle system?
(d) What are the quantum state vectors of the first excited state?
(e) What is the degeneracy of the first excited state?
(f) Discuss qualitatively how the excited-state energies change if we consider the particles
to be interacting through the Coulomb potential.
Transcribed Image Text:Problem 4. Consider two indistinguishable, noninteracting spin-1/2 fermions in a one- dimensional infinite square well potential of length L. (a) What is the ground-state energy of the two-particle system? (b) What is the ground-state quantum state vector? (c) What is the first excited state energy of the two-particle system? (d) What are the quantum state vectors of the first excited state? (e) What is the degeneracy of the first excited state? (f) Discuss qualitatively how the excited-state energies change if we consider the particles to be interacting through the Coulomb potential.
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