Suppose we add a certain amount of energy to a quanton in a box, 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} .

Question

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The energy levels in a quantum system like a particle in a box are quantized and not equally spaced. The energy difference between levels increases with higher energy states, so the same amount of energy may not be sufficient to move from $E_{n+1}$ to $E_{n+2}$ as it was to move from $E_{n}$ to $E_{n+1}$.

Suppose We Add a Certain Amount of Energy to a Quanton