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For a single particle of a monatomic ideal gas, the partition function is derived from the principles of statistical mechanics. A monatomic particle has only translational degrees of freedom, and its energy is purely kinetic. The energy of a particle in three dimensions is given by ( \varepsilon = \frac{p_x^2}{2m} + \frac{p_y^2}{2m} + \frac{p_z^2}{2m} ), where ( p_x, p_y, p_z ) are the momentum components ________ ________ _____ _______ _________.
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