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For a quantum confinement model, the wave function of a particle is zerooutside the confined region. Due to this, the negative energy states are, infact, square integrable. As negative energy states are not physical, we need toimpose some boundary conditions in order to avoid these states. For the case ofthe infinite square well model, we show the possible boundary conditions thatavoid the existence of the negative energy states. The well-known boundarycondition requiring the wave function be continuous on both sides of the wellis one of the boundary conditions that avoids negative energy states. However,there are other types of boundary condition that can also avoid the negativeenergy states. This shows that there are the different branch of physicalsystems that can be established on the infinite square well model.

On the boundary conditions for eliminating negative energy states in the infinite square well model