# Collapse of the wave function, help understand

• Lengalicious
In summary, the collapse of the wave function is a concept in quantum mechanics that helps to explain how a particle's properties are determined when measured. It states that the wave function, which describes the probability of finding a particle in a certain state, collapses to a single state upon measurement. This phenomenon helps to understand the unpredictable nature of quantum particles and has implications for the understanding of reality at a fundamental level.
Lengalicious
Ok so when observed, the wavefunction collapses, can someone delicately explain the maths behind it? Or send me to a page with a coherent explanation, that is followable for a first year undergrad? I've covered Eigenvectors briefly in my algebra course last semester and i find that the explanations focus on some eigenvector stuff but i don't completely understand what an eigenvector is, just how to get an eigen vector/value. All i know is that the wave function decreases with path difference and therefore decreases the probability of the particle being at that particular point. But the fact that randomly when a detector interacts with the particle the wavefunction collapses and it acts as a classical particle is confusing me. Whyy? =(

Lengalicious said:
Ok so when observed, the wavefunction collapses, can someone delicately explain the maths behind it? Or send me to a page with a coherent explanation, that is followable for a first year undergrad? I've covered Eigenvectors briefly in my algebra course last semester and i find that the explanations focus on some eigenvector stuff but i don't completely understand what an eigenvector is, just how to get an eigen vector/value. All i know is that the wave function decreases with path difference and therefore decreases the probability of the particle being at that particular point. But the fact that randomly when a detector interacts with the particle the wavefunction collapses and it acts as a classical particle is confusing me. Whyy? =(
The wave function does not really collapse. It only splits into distinguishable branches, so that any branch does not know about the existence of the others. The right question is why can't we see all the branches at once?

One possible answer is - because we ARE one of the branches (many-world interpretation).

Another possible answer - because we are made of little particles which end up in one of the branches (Bohmian interpretation).

There are also other possible answers, but nobody knows which one is correct.

If you want more math behind it, see e.g. Sec. 2 of
http://xxx.lanl.gov/abs/1112.2034

## 1. What is the collapse of the wave function?

The collapse of the wave function is a fundamental concept in quantum mechanics that describes the transition of a quantum system from a state of multiple possible outcomes to a single definite outcome when it is observed or measured.

## 2. How does the collapse of the wave function occur?

The exact mechanism of the collapse of the wave function is still a topic of debate and is one of the major unresolved issues in quantum mechanics. Some theories suggest that it is a spontaneous process that occurs randomly, while others propose that it is influenced by the observer's consciousness or the act of measurement itself.

## 3. What is the role of observation in the collapse of the wave function?

In quantum mechanics, the act of observation or measurement plays a crucial role in the collapse of the wave function. It is believed that the act of observation causes the wave function to collapse, and the quantum system to assume a definite state. This is known as the measurement problem and is still a subject of ongoing research and debate.

## 4. Can the collapse of the wave function be predicted or controlled?

No, the collapse of the wave function is a probabilistic event and cannot be predicted or controlled with certainty. The outcome of a quantum system can only be described in terms of probabilities, and the exact outcome cannot be known until it is observed or measured.

## 5. How does the collapse of the wave function relate to the uncertainty principle?

The collapse of the wave function is closely related to the uncertainty principle, which states that it is impossible to know both the position and momentum of a particle with absolute certainty. This is because the act of measuring one quantity will inevitably disturb the other, causing the wave function to collapse and the outcome to become uncertain.

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