Bad Qubits — Learn Quantum by Doing

Multiple choice

For the quantum harmonic oscillator with energy levels E_n = hbar*omega*(n + 1/2), how does the fractional energy spacing Delta E / E_n between adjacent levels behave as the quantum number n grows large?

It oscillates between 0 and 1 without settling to any limit
It grows linearly with n, making the levels easier to resolve
It vanishes like 1/n, so the discrete spectrum mimics a continuous one
It stays fixed at 1/2 for every value of n