# Expectation value of P for an infinite-square well

• jmm5872
In summary, the expectation value of P for an infinite-square well is the average value of the momentum of a particle in the well. It is calculated by taking the integral of the momentum operator and dividing it by the square of the wave function. This value represents the most likely or average momentum of a particle in the well. It is not a constant value and can vary depending on the energy level of the particle. As the width of the well increases, the expectation value of P also increases due to a wider range of possible momentum values.
jmm5872
I just have a simple question to get me started. If I am given an initial value wavefunction ψ(x,0) and I am asked to find <P> at t = 0 can I use this:

<P> = -ih∫ψ*(x,0)$\frac{∂}{∂x}$ψ(x,0)dx

or do I need to find ψ(x,t) before I find <P>?

No you are right (h bar)

## 1. What is the expectation value of P for an infinite-square well?

The expectation value of P for an infinite-square well refers to the average value of the momentum of a particle in the well. It is a mathematical concept used to describe the behavior of quantum particles in a confined space.

## 2. How is the expectation value of P calculated for an infinite-square well?

The expectation value of P is calculated by taking the integral of the momentum operator over the entire space of the infinite-square well. This integral is then divided by the square of the wave function, which gives us the average value of the momentum.

## 3. What does the expectation value of P represent in an infinite-square well?

The expectation value of P represents the most likely value of the momentum that a particle will have in an infinite-square well. It can also be interpreted as the average momentum of a large number of particles in the well.

## 4. Is the expectation value of P for an infinite-square well a constant value?

No, the expectation value of P can vary depending on the energy level of the particle in the well. As the energy level increases, the expectation value of P also increases.

## 5. How does the expectation value of P change as the width of the infinite-square well increases?

As the width of the infinite-square well increases, the expectation value of P also increases. This is because a wider well allows for a larger range of momentum values, resulting in a higher average momentum for the particle.

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