# Confirming Symmetric & Antisymmetric Solutions for Wave Function

• Cosmossos
In summary, the conversation is about confirming the correctness of a potential and solving equations for symmetric and antisymmetric states in relation to the potential. The original poster is seeking help and expresses feeling hopeless.
Cosmossos

## Homework Statement

Hello,
Can you confirm that what I wrote is correct for the given potential?
https://www.physicsforums.com/attachment.php?attachmentid=22309&stc=1&d=1260118852

Now I wrote the term for the wave funcation and for the given symetric potential , the functions of the serdinger equation are symetric.so for the symmetric state - Psi (s) and the antisymmetric state Psi(a) I need to show that the energy of the symetric state is given by solving the following equations:
http://www.zix.co.il/images/630087545.JPG

thanks

## The Attempt at a Solution

What is the potential?

The potentials is V in first picture

The first picture is either not loaded properly or is not a valid attachment. Can you write what it is?

Here is another try

## 1. What is a wave function?

A wave function is a mathematical function that describes the quantum state of a system. It represents the probability amplitude of a particle's position, momentum, and other physical properties.

## 2. What is a symmetric solution for a wave function?

A symmetric solution for a wave function means that the wave function remains unchanged when the position of the particle is exchanged with another identical particle. In other words, the probability of finding the particle at a certain position is the same regardless of which particle is being observed.

## 3. What is an antisymmetric solution for a wave function?

An antisymmetric solution for a wave function means that the wave function changes sign when the position of the particle is exchanged with another identical particle. In other words, the probability of finding the particle at a certain position is opposite for different particles.

## 4. How do you confirm if a wave function has symmetric or antisymmetric solutions?

To confirm if a wave function has symmetric or antisymmetric solutions, you can use the symmetry operator. If the wave function remains unchanged when the symmetry operator is applied, then it has a symmetric solution. If the wave function changes sign when the symmetry operator is applied, then it has an antisymmetric solution.

## 5. Why is it important to confirm the symmetry of wave function solutions?

Confirming the symmetry of wave function solutions is important because it helps us understand the behavior of particles and the laws of quantum mechanics. It also allows us to accurately predict the behavior of particles in various situations and make accurate calculations in quantum systems.

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