Confirming Symmetric & Antisymmetric Solutions for Wave Function

[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

Please help me , I'm hopeless.
thanks

Homework Equations

The Attempt at a Solution

 

[Matterwave]

What is the potential?

 

[Cosmossos]

The potentials is V in first picture

 

[jdwood983]

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

 

[Cosmossos]

Here is another try