A system of 9 identical non-interacting spin-3/2 particles confined to a one-dimensional harmonic oscillator potential is in its minimum energy configuration for which $ E = 5.75 \, \text{eV} $. What is the minimum energy of the same system with 10 such particles? Recall that the energy levels of a single particle in a one-dimensional harmonic oscillator potential are given by $ E_n = \left( n + \frac{1}{2} \right) \hbar \omega_0 $ with $ n = 0, 1, 2, \ldots $.

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