This Demonstration studies a transition from the ground state to the excited state. The quantum wave oscillating with the period between the two states, where and are time-dependent functions and is related to the strength of the external field. For the wavefunction in the ground state gives an exact solution to the Schrödinger equation. The model used is that of (spinless) quantum particles in a one-dimensional harmonic oscillator potential (described by normalized solutions of the corresponding Schrödinger equation) involving products of Hermite polynomials with a Gaussian function. According to the orthodox interpretation of quantum theory, the energy of the system, which is in a superposition of states, will not have a definite value (except for integer multiples of the period) for an ensemble of noninteracting quantum particles until a measurement is carried out. Therefore, a measurement of the energy at time will give either or , with probabilities and , respectively.

In the causal interpretation, ensembles of particles are characterized by a wavefunction, an initial position, and a trajectory. The trajectories are streamlines in the Madelung fluid, regarded as paths of quantum particles that are not directly measurable because of the perturbation caused by the measurement process. In the superposition of states, the energy for each individual quantum particle evolves in a continuous manner. The particle's motion evolves such that its energy equals or , depending on its initial position.