ASSIGNED: FRI 25 JAN

DUE: FRI 01 FEB

In all problems the Mathematica output is part of your grade and must be turned in with your paper and pencil calculations.

For the Mathematica calculations, such as in the Integrate command, you need to specify that the constants such as a, σ, λ, etc., are real numbers greater than zero or else it will assume they are complex numbers and produce crazy looking answers. To do this read the "tutorial/UsingAssumptions" which you will find in the Mathematica Help / Documentation Center.

1. GRIFFITHS PROBLEM 2.4, PAGE 38: First carry out the integrals by hand using lookup tables and then do them again using the Integrate function and derivative function D in Mathematica. Hint: You need the formulas from CH01.5 as well as EQ02.28. You may find it handy to learn Speed Integration by Parts!

2. GRIFFITHS PROBLEM 2.5, PAGE 38: Again carry out the calculations first by hand using paper and pencil and an integral lookup table and then again using the Integrate function in Mathematica. For parts (b) and (c) use the Manipulate and Animate functions to produce animated plots of the probability density |Ψ(x,t)|

3. GRIFFITHS PROBLEM 2.6, PAGE 39. Again carry out the calculations first by hand using paper and pencil and an integral lookup table and then again using the Integrate function in Mathematica. Use the Manipulate and Animate functions to produce animated plots of the probability density |Ψ(x,t)|

4. GRIFFITHS PROBLEM 2.7, PAGE 39. Again carry out the calculations first by hand using paper and pencil and an integral lookup table and then again using the Integrate function in Mathematica. For part (b) use the Manipulate and Animate functions to produce animated plots of the probability density |Ψ(x,t)|

5. GRIFFITHS PROBLEM 2.8, PAGE 40. Again carry out the calculations first by hand using paper and pencil and an integral lookup table and then again using Integrate function in Mathematica. Hint: This is a rehash of EX02.2 and EX02.3 for t=0 with a new Initial Condition Ψ(x,0) that needs to be expanded in a sum of the eigenfunctions ψ

6. GRIFFITHS PROBLEM 2.9, PAGE 40. Again carry out the calculations first by hand using paper and pencil and an integral lookup table and then again using Integrate function in Mathematica. Hint: He means for you to use EQ02.11 and then carry out the derivatives and then integrate against the function Ψ(x,0) from page 35, using the value of the normalization constant A from page 36.