The statement that solutions to the quantum harmonic oscillator have discrete energy levels and zero-point energy is a fundamental, textbook result of quantum mechanics that requires no citation.
This statement represents a textbook physical definition and foundational truth of quantum mechanics (specifically, the solution to the Schrödinger equation for a quadratic potential yielding $E_n = \hbar \omega (n + 1/2)$). Under Step 0, statements that are trivially true by definition or direct disciplinary observation are classified as COMMON_KNOWLEDGE.