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## Main Question or Discussion Point

In my text book, it says "For a system of one-dimensional oscillators, the energy levels are equally spaced and non-degenerate, so the number of quantum states in an interval dE is proportional to

1. Why are the energy levels are equally spaced? According to the Bohr Model of hydrogen, as the energy level is getting higher, the distance between two levels are getting closer.

2. Why should it be non-degenerate? What's the difference between degenerate and non-degenerate energy levels?

3. Why is

Can someone help to explain a bit on these?

*dE*so long as*dE*is much larger than the spacing*h(h-bar)w*between levels. In fact, we may conclude from this that*g(E)dE*must have the value*dE/h(h-bar)w*."1. Why are the energy levels are equally spaced? According to the Bohr Model of hydrogen, as the energy level is getting higher, the distance between two levels are getting closer.

2. Why should it be non-degenerate? What's the difference between degenerate and non-degenerate energy levels?

3. Why is

*h(h-bar)w*the spacing and as long as*dE*is much larger than it, the number of quantum states in an interval*dE*is proportional to*dE*? Also,*dE*is just the differential of energy, it should have no size and thus can't be measured to be compared with the spacing.Can someone help to explain a bit on these?