Time evolution of nodes in quantum superposition states

The nodes are traditionally viewed as fixed points where the probability density vanishes. However, this work demonstrates that these nodes exhibit time-dependent oscillation in quantum superposition states. We derive this effect for a fundamental system: the 1D particle in a box. It is shown that the probability density in a superposition of two eigenstates evolves with a time-dependent interference term, introducing an oscillation of the nodes at a specific frequency equal to the energy difference between the states. This result suggests a deeper dynamical role for nodes in quantum systems.