Discussion
For a simple harmonic oscillator :
Answer: D
For a simple harmonic oscillator, the number of nodes of the wave function increases with increase in energy.
The wave function of level v has exactly v nodes: none for v = 0, one for v = 1, and so on, the same pattern as for a particle in a box.
The levels Ev = (v + 1/2)hν are equally spaced, so the spacing neither increases (B) nor decreases (C); decreasing spacing belongs to the anharmonic oscillator. The potential energy V = kx2/2 rises with the square of the displacement, not linearly (A).
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