HW02

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)|2 and the time-dependent expectation value <x(t)> as shown in EX02.2.NB. Hints: ψ1 and ψ2 are from EQ02.28. Figure out who the heck Peter Lorre is and then use EQ01.33.

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)|2 for the case φ=π/2 and again for φ=π and compare the two results.

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)|2. Hints: This is a variation on EX02.2 and EX02.3, which was worked out in detail by hand in the notes and for which I made two Mathematica notebooks for you to study.

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 ψn(x) and in terms of NEW expansion coefficients cn.

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.