In the context of quantum mechanics, the observation that the peak intensity in a double-slit experiment is 4 times higher than in the single-slit case can be explained by considering the probabilistic nature of particles and the concept of wave-particle duality.
In quantum mechanics, particles such as photons (light particles) can exhibit both particle-like and wave-like properties. When a beam of light passes through a single slit, it diffracts and spreads out, creating a pattern of light and dark regions on a screen. This is consistent with the wave-like behavior of light.
In the double-slit experiment, when a beam of light is directed at two slits close together, each slit acts as a source of a new wavefront. These wavefronts then interfere with each other, leading to the formation of an interference pattern on the screen. The interference occurs due to the superposition of the probability amplitudes associated with different paths the photons can take.
According to quantum mechanics, the intensity of light at a given point on the screen is related to the square of the probability amplitude associated with that point. When the two wavefronts interfere constructively (peaks aligning with peaks), the probability amplitudes add up, resulting in an increased intensity compared to the single-slit case. This constructive interference leads to the bright fringes in the interference pattern.
However, it is important to note that the intensity in quantum mechanics is not simply additive as in classical physics. Instead, it is related to the probabilities associated with different outcomes. In the double-slit experiment, the intensity at the bright fringes is four times higher than the intensity in the single-slit case because the probability amplitudes from the two slits add up coherently, resulting in a higher probability of photons being detected at those locations.
Therefore, the observation that the peak intensity in the double-slit experiment is 4 times higher than in the single-slit case can be explained in quantum mechanics by considering the interference of probability amplitudes associated with different paths, leading to constructive interference and a higher probability of detecting photons at certain locations on the screen.