Regeneration of wave function

[San K]

in a double slit single particle interference experiment:

when we try to find out which-way the "wave-function collapses"...however does the wave function "start to form" again once the photon/electron leaves the slits?

or is sending sending the photon through another set of double (or triple, quad etc) slits/paths the only way to regenerate the wave-function?

we know that a wave-function is a mathematical/theoretical tool and no one knows what happens in reality yet...however how is the wave-function regeneration mathematically/theoretically viewed within the concept?

 

[eljose79]

Thank you for your interesting question about the behavior of the wave-function in a double slit single particle interference experiment.

Firstly, let's clarify what we mean by the "collapse" of the wave-function. This term is often used to describe the change in the probability distribution of a particle's position when it is measured. In other words, when we observe the particle's position, the wave-function "collapses" into a specific location. This is a fundamental aspect of quantum mechanics and is still an active area of research and debate.

Now, to answer your question about the regeneration of the wave-function. It is important to note that the wave-function never truly disappears or "starts to form" again. It is a mathematical representation of the state of the particle and is always present. However, the behavior of the wave-function can change depending on the experimental setup.

In a double slit single particle interference experiment, the wave-function of the particle can be thought of as a probability distribution of where the particle is likely to be found. When the particle passes through the slits, it behaves like a wave and interferes with itself, creating an interference pattern on the detector screen. This is known as the "wave-like" behavior of the particle.

However, when we try to determine which slit the particle went through, we are essentially "measuring" the particle's position. This causes the wave-function to collapse into a specific location, and the interference pattern disappears. This is known as the "particle-like" behavior of the particle.

In terms of regeneration, sending the particle through another set of double slits or paths is not the only way to restore the interference pattern. In fact, simply removing the measuring device or not collecting the measurement data can also allow the wave-function to "regenerate" and the interference pattern to reappear. This is known as the "quantum eraser" experiment.

In conclusion, the wave-function is always present and its behavior depends on the experimental setup and our actions as observers. The concept of regeneration is not necessary, as the wave-function is a fundamental aspect of quantum mechanics and is constantly evolving and changing in response to measurements and interactions. I hope this helps to clarify your understanding of the wave-function in the context of a double slit single particle interference experiment.