# One quantum particle, many boxes

• Axiom17
In summary, the conversation discusses how to find the probability of finding a quantum particle in each of two identical boxes, given a specific wavefunction. By using the probability density formula and normalizing the probabilities, it is determined that the probability of finding the particle in the second box is 2/9.
Axiom17

## Homework Statement

A quantum particle is described by the wavefunction $\psi(r)$. There are 2 identical boxes (A & B).. what's the probability of finding the particle in each box?

## Homework Equations

$$\psi(r)= \left\{ {\begin{array}{ll} 1+i & if A\\ 1-i & if B\\ 0 & if elsewhere\\ \end{array}} \right$$

## The Attempt at a Solution

I'm really not sure where to start with this I see that I have the wavefunction $\psi$ for each box (and elsewhere), but I'm not sure what to do as far as the calculations.. hopefully just need a bit of a hint to get me going with it.

Last edited:
Sorry, but I don't know how to use Latex, so please try to follow what I think:

|psi|² is the probability density, let's call it P1 for the first box, P2 for the second en P3 for the third.

P1=(1-2i)(1+2i)=5
P2=(1-i)(1+i)=2
P3=(1+i)(1-i)=P2=2

Because the probability is normalized, we have to divide by P1+P2+P3=9 to get p1, p2 and p3. This gives that the probability p2 to find it in the second box is 2/9.

Ok thanks for that I get it now

## 1. What does the concept of "one quantum particle, many boxes" mean?

The concept of "one quantum particle, many boxes" refers to the idea in quantum mechanics that a single particle can exist in multiple locations or states at the same time. This phenomenon is known as quantum superposition.

## 2. How does quantum superposition work in this scenario?

In the case of "one quantum particle, many boxes", the particle is said to exist in a superposition of states, meaning it has a probability of being in any one of the boxes at a given time. This probability is described by a mathematical function known as the wave function.

## 3. What is the significance of this concept in quantum mechanics?

The concept of "one quantum particle, many boxes" is significant because it challenges our traditional understanding of particles and their behavior. It also has practical applications in quantum computing and cryptography.

## 4. Can this concept be observed in real-life scenarios?

Yes, the phenomenon of quantum superposition has been observed in various experiments, such as the double-slit experiment. However, observing it in macroscopic objects is challenging due to the delicate nature of quantum systems.

## 5. How does this concept relate to the uncertainty principle?

The uncertainty principle states that it is impossible to know the exact position and momentum of a particle simultaneously. In the case of "one quantum particle, many boxes", this principle is evident as the particle can exist in multiple positions at the same time, making it impossible to determine its exact location.

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