3 non-interacting fermions are confined in a 2-D box of area andlsquo;a2. If the energy of the 1st excited state of thesystem isCorrect answer is '12'. Can you explain this answer?

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3 non-interacting fermions are confined in a 2-D box of area ‘a^2'. If the energy' of the 1st excited state of the system is

Correct answer is '12'. Can you explain this answer?

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3 non-interacting fermions are confined in a 2-D box of area ‘a2...

Energy of a particle in a 2-D box is

where,

is ground state,

is the 1st excited state.
Therefore, 1st excited state has one fermion each in (1,1), (1,2), (2,1) levels.

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3 non-interacting fermions are confined in a 2-D box of area ‘a2'. If the energy' of the 1st excited state of thesystem isCorrect answer is '12'. Can you explain this answer?

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