1. a Show how the separation of variables takes place for a two dimensional particle in a box. Be very precise in your explanation.

1 b What would the eigenvalue and function be for the second lowest energy state for an electron in a square potential well with sides of 0.1 nm.

1 c. Sketch what this function would look like.

2. Show that Y₁₂ is orthogonal to Y₂₁ for a 2 D PIB with functions given like equation 9.94.

3. For a 2 dimensional partical in a box, show that the function Y= aY₁₂ + aY₂₁ satisfys the Shrodinger equation if a is a constant.

4. Show that a in #3 must be equal to the square root of 2.

5. Show that Y= aY₁₂ + aY₂₁ is orthogonal to Y= aY₁₂ -aY₂₁ but is not orthogonal to Y₁₂ .

6. Discuss the implications of #5. What is the generacy of the 21 state. How many eigenfunctions can have the 21 energy. How may sets of eigenfunctions could satisfy the 21 energy.