Suppose we add a certain amount of energy to a simple quantum harmonic oscillator, increasing its energy from $E_{n}$ to $E_{n+1}$. Adding the same amount of energy again will increase its energy to $E_{n+2}$.

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In a quantum harmonic oscillator, the energy levels are quantized and equally spaced. Adding the same amount of energy moves the system from one quantized energy level to the next, so going from $E_{n}$ to $E_{n+1}$ and then to $E_{n+2}$ with equal energy increments is consistent with the quantum mechanical model.

Suppose We Add a Certain Amount of Energy to a Simple