Could the situation depicted in the following diagram repres

Could the situation depicted in the following diagram represent a particle in a bound state? Explain.

Solution

Bound states results when

(a) The potential U(x) has a minimum as we plot it.

(b) The total energy E of the particle is larger than the minimum, but lower than any maximum on either side of the minimum.

In bound state, the eigenfunction is confined to a finite region, outside which its absolute value drops rapidly.

The figure in the question satisfies these conditions and the particle is bound in the region between the two high potentials. Hence it is a bound state.