# Probability inside finite square well

• kraigandrews
In summary, the probability of a particle being in the first third of a well while in the ground state is related to the wave function. By squaring the wave function and integrating from 0 to L/3, the probability can be determined. It is important to ensure that the correct wave function is used for the specific type of well.
kraigandrews

## Homework Statement

What is the probability, that the particle is in the first third of the well, when it is in the ground state?

## Homework Equations

$\Psi$(x)=Asin((n*pi)/L)

A=(2/L)1/2

## The Attempt at a Solution

so probablility is related to the wave function by $\Psi$2

so i would think it would just be square the wave function and integrate from 0 to 1/3

That seems right to me.

The upper limit should be L/3. Make sure you have the correct wave function. The wave function you have is for the infinite square well (and is missing an x), but the title of the thread mentions the finite square well.

## 1. What is a finite square well?

A finite square well is a mathematical model that describes the potential energy of a particle inside a finite region. It is often used in quantum mechanics to study the behavior of particles confined in a certain space.

## 2. How is probability calculated inside a finite square well?

The probability inside a finite square well is calculated using the Schrödinger equation, which takes into account the potential energy of the particle and the boundary conditions of the well. The solution to this equation gives the probability distribution of finding the particle at a certain position inside the well.

## 3. What are the factors that affect the probability inside a finite square well?

The probability inside a finite square well is affected by the depth and width of the well, as well as the energy of the particle. It is also influenced by the shape of the potential energy barrier and any external forces acting on the particle.

## 4. Can the probability inside a finite square well be greater than 1?

No, the probability inside a finite square well cannot be greater than 1. This is because the total probability of finding the particle inside the well must be equal to 1, as it is the only possible location for the particle to be in.

## 5. How does the probability inside a finite square well change with time?

The probability inside a finite square well may change with time if the potential energy of the well is time-dependent. In this case, the Schrödinger equation must be solved for different times to determine how the probability distribution evolves over time.

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