# Perturbation in Infinite Square well

• ed2288
In summary, the problem at hand requires the calculation of the 1st order probability of finding an electron in the first excited state of an infinite square well, after the perturbation H=sin(PI*x) is switched on. This can be solved by using the time-dependent perturbation theory and the transition frequency to determine the probability at time t seconds. The wavefunction squared should be used instead of the product of two wavefunctions, and the time-dependent Schrodinger equation should be considered for accurate results.
ed2288

## Homework Statement

Calculate the 1st order probability an electron in the ground state of an infinite sqaure well (width 1) will be found in the first excited state t seconds after the pertubation H=sin(PI*x) is switched on.

## Homework Equations

Transition frequency is omega_12

## The Attempt at a Solution

I know to begin this question I need to calculate the integral between 0 and 1 of the product of the ground state wavefunction, pertubation, and 1st excitied wavefunction. The product comes to sin^2(PI*x)sin(2PI*x), which when integrated comes to zero!
Any suggestions??
Thanks
(ps I know that this integral will not give the final answer, but I know exactly what to do after this step)

Hello,

Thank you for your post. It seems like you are on the right track with your approach. However, there are a few things to consider in order to get the correct answer.

First, when calculating the probability of finding an electron in a particular energy state, we use the wavefunction squared, rather than the product of two wavefunctions. This is because the wavefunction squared gives us the probability density, which tells us the likelihood of finding the electron in a particular position.

Second, in order to calculate the probability at a specific time t, we need to use the time-dependent Schrodinger equation. This equation takes into account the time evolution of the wavefunction and allows us to calculate the probability at any given time.

In this case, we can use the time-dependent perturbation theory to solve for the probability at t seconds after the perturbation is switched on. This involves expanding the wavefunction in terms of the unperturbed states and using the transition frequency to determine the probability at the desired time.

I hope this helps guide you in the right direction. If you have any further questions, please let me know.

## What is perturbation in an infinite square well?

Perturbation in an infinite square well refers to a small disturbance or change in the potential energy of a quantum system, specifically in the context of an infinite square well potential. This perturbation can cause the energy levels and wavefunctions of the system to shift or change.

## What causes perturbation in an infinite square well?

Perturbation in an infinite square well can be caused by external factors such as an applied electric or magnetic field, or by internal factors such as a change in the potential energy function due to a moving boundary or a change in the particle mass.

## How does perturbation affect the energy levels in an infinite square well?

Depending on the magnitude and nature of the perturbation, it can either cause the energy levels to shift or split into multiple levels. This is known as energy level splitting or degeneracy lifting. The amount of splitting depends on the strength of the perturbation and the energy level it is acting on.

## What is the perturbation theory in an infinite square well?

Perturbation theory in an infinite square well is a mathematical tool used to analyze and calculate the effects of a small perturbation on the energy levels and wavefunctions of a quantum system. It involves expanding the perturbation term as a series and solving for the corrections to the unperturbed system.

## How is perturbation in an infinite square well used in real-world applications?

Perturbation in an infinite square well has various applications in different fields such as quantum mechanics, solid state physics, and chemistry. It is used to model and study the behavior of particles in confined systems, and also to understand the effects of external factors on these systems. It is also used in the design and development of quantum computing devices.

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