Yes, in the double-slit experiment, the results obtained in conjunction with the Schrödinger equation show that certain bands of light are more likely to receive more hits of photons when an interference effect is observed.
In the double-slit experiment, a beam of particles (such as photons or electrons) is directed at a barrier with two narrow slits. Behind the barrier, a screen is placed to observe the pattern formed by the particles that pass through the slits. Surprisingly, even when particles are sent through the slits one at a time, an interference pattern emerges on the screen, indicating that the particles exhibit wave-like behavior.
The behavior of particles in the double-slit experiment can be described mathematically using the Schrödinger equation, which is a fundamental equation in quantum mechanics that describes the behavior of quantum systems. When applied to the double-slit experiment, the Schrödinger equation predicts the existence of wave functions that describe the probability distribution of the particles.
The interference pattern arises from the constructive and destructive interference of the wave functions associated with the particles passing through the slits. Wherever two wave functions overlap and interfere constructively, there is a higher probability of detecting a particle at that location on the screen. Conversely, where destructive interference occurs, the probability of detecting a particle is lower.
The intensity of light in a given region on the screen, which corresponds to the number of photons hitting that region, is proportional to the square of the wave function's magnitude. Therefore, regions with constructive interference will have higher intensities and are more likely to receive more hits of photons, while regions with destructive interference will have lower intensities and are less likely to receive photon hits.
This phenomenon demonstrates the wave-particle duality of quantum systems. Even though individual particles are detected as discrete entities, their overall behavior, as described by the wave function, exhibits wave-like interference patterns. The Schrödinger equation provides a mathematical framework to understand and predict these patterns in the context of quantum mechanics.