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