Question

In the double-slit experiment, the interference pattern shows the probability of finding the particle (photon or electron) at a given volume. In a given experimental setting, this probability distribution doesn't change with time, so this probability distribution belongs to a stationary quantum state. I think that this doesn't mean that the Hamilton operator belonging to an experimental setting has only one eigenvalue and a single state that belongs to this eigenvalue because the pattern depends on the wavelength of the photon. If we used the superposition of two photons of different wavelengths, we would get a non-stationary interference pattern. Is there such a thing as the superposition of two photons of different wavelengths? Or the double-slit experiment can't produce non-stationary states?

Answer 1

The superposition of photons of different wavelengths is theoretically possible, leading to non-stationary interference patterns in the double-slit experiment. However, the practical realization and detection of such superpositions remain highly challenging due to technical limitations.

Step-by-step explanation:

The double-slit experiment demonstrates the wave-like nature of particles, exhibiting interference patterns characteristic of stationary quantum states. This stationary behavior arises from the consistent wavelength associated with the photons or electrons used. However, the superposition principle in quantum mechanics allows for combining states, including different photon wavelengths.

Theoretically, combining two photons with distinct wavelengths can lead to a non-stationary state, altering the interference pattern observed. Yet, practically realizing such a superposition and detecting it poses significant experimental challenges. The ability to generate and control photons of different wavelengths in a superposition state with high precision remains an ongoing area of exploration and technological advancement within quantum physics.

While theoretically conceivable, the practical implementation of superposing photons of different wavelengths in the double-slit experiment and observing resultant non-stationary states presents considerable experimental hurdles due to current limitations in controlling such quantum states and precise measurements of their interference patterns.