# The Superposition Principle in the Causal Interpretation of Quantum Mechanics

The Superposition Principle in the Causal Interpretation of Quantum Mechanics

The principle of quantum superposition states that the complex-valued wavefunction can be a linear combination of several quantum eigenstates simultaneously. The modulus (or absolute value) squared of the total wave function represents a probability density of finding a quantum particle only. In the causal interpretation of quantum theory, developed in 1952 by David Bohm, the concept of trajectories is introduced, in which the particles are guided by a real phase function (or quantum potential) from the total wavefunction (pilot wave). In the eikonal representation, the phase function for a superposed state from which the velocity is determined becomes very complicated. This Demonstration discusses a superposition of up to 15 states of the density distribution for a quantum particle in the box with infinitely high walls. As the superposed wave packet spreads in an infinite square well, the paths of the quantum particles approach in a way similar to a classical trajectory.

The graphic shows the squared wavefunction, the possible trajectories of six quantum particles, and the contour plot of the quantum potential. Light areas correspond to large probability density whereas dark areas represent a low probability of finding a particle.