Bad Qubits — Learn Quantum by Doing

Multiple choice

In the WKB connection formulas, applying the matching at both turning points of a bound state yields the Bohr-Sommerfeld quantization rule integral(p dx) = (n + 1/2) pi hbar. Where does the famous +1/2 come from for two smooth (linear) turning points?

From a pi/4 phase shift picked up at each smooth turning point, giving pi/2 in total
From the de Broglie wavelength being exactly equal to hbar at the turning point
From the requirement that the energy be negative
From the normalization of the wavefunction at the origin