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I understand about the close-spacing of the translational/rotational energy
levels and can see why the gaseous state allows many more energy levels than
the liquid state. However, I fail to understand how the spreading of the
gas molecules into a greater volume results in a greater number of possible
energy levels.
It's a straightforward extension of the quantum mech analysis of the energy
levels available to a particle in a box. A particle in a larger box has
similar wave functions but they are closer together, thus, energetically, they
are more accessible for molecules -- without any greater total energy than
when they were in a smaller box.
This I know to be true qualitatively -- from reading and talking with quant
mech guys.
But you, as a physicist, could help me (and yourself) by checking QM texts or
physics QM people and telling me about some details of this "energy levels of
particles in a small vs.a large box" case: First, I know and it is common
knowledge that translational energy levels are so close together that they
cannot be individually determined spectroscopically (the way other energy
levels are quantitatively established -- rotational in the IR spectra, and
vibrational there also (in the shorter IR), whereas excitational are in the
visible and UV). But can those translational energy levels be experimentally
detected "as a group", let's say, or some other packet? i.e., is there
experimental data to prove this "closer levels in large than small box" QM
idea, or is it totally from calculations/theory?