 Solution

For a symmetric finite well supporting this excited bound state, the wavefunction and its derivative match continuously at each finite potential step. Outside, where $V_{\mathrm{wall}}>E$, the solution decays exponentially withThe density therefore extends into the classically forbidden region instead of dropping to zero at the walls. Its interior lobes and normalization change, and the energy is lower than for the corresponding infinite-wall state at the same well bottom. Symmetry preserves the central node for the first excited state. The diagram shows an explicitly illustrative barrier height, not an extra numerical value supplied by the question.