Calculating the probability density |ψ(x)|² is sufficient to determine if a quantum particle crosses a barrier. However, probability current density is essential for understanding the conservation of probability, particularly in scenarios involving boundaries. While it is often overlooked, current density provides insight into the flow of probability, which is crucial for a complete analysis. The discussion emphasizes that while probability density can indicate presence, current density is necessary for a deeper understanding of quantum behavior. Thus, both concepts serve distinct but important roles in quantum mechanics.