only need help with B and C (i.e. understand what the basis is, don\'t know how

Question

only need help with B and C (i.e. understand what the basis is, don't know how to notate it)

Consider the state of three particles in a system with three single-particle states (orbitals) a Wb andve (a) If the particles are distinguishable, show that the Hilbert space dimension is 27 (i.e. the Hilbert space is spanned by 27 basis states). (b) Write down an orthonormal basis for the Hilbert space of 3 identical bosons in this system. (b) Write down an orthonormal basis for the Hilbert space of 3 identical fermions in this system.

Explanation / Answer

Fermions are particles which obey Pauli exclusion principle which which say that no 2 spin half particles can be accommodated in 1 state/have all Quantum numbers same.

Bosons have no such constraint therefore any number of particles can be in a state.

As here are only 3 particles.

Orthonormal means whose inner product vanishes and they are normalised.

Also provided three bosons are identical i e indistinguishable.hence,

These are written in ket-bra notation developed by Dirac.

Bosons :1/7{3 |111,0,0>+3|11,1,0>+|1,1,1>} 3

Fermions: |1,1,1> only state

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