ASSIGNED: FRI 01 FEB

DUE:

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 2.11, PAGE 50: 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 may find some of the formulas in CH2.3.1 useful.

2. GRIFFITHS PROBLEM 2.13, PAGE 50: 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 wave function Ψ(x,t) and the probability density |Ψ(x,t)|

3. GRIFFITHS PROBLEM 2.15, PAGE 57. Hint: Skip the math table and use Mathematica to carry out the integral, which is the area under the curve in the "wings" of |ψ

4. GRIFFITHS PROBLEM 2.16, PAGE 57. Again carry out the calculations first by hand using paper and pencil and algebra and then write a Mathematica code to do the same.

5. GRIFFITHS PROBLEM 2.17, PAGE 57. Do it by hand and then again in Mathematica. Hint: Take a look-see at CH02.3.NB.

7. A Quantum SHO is in the initial state Ψ[x,0]=f[x]=B*Sin[x]*Exp[–x^2/2] = f[x], where we have taken the unit of length l=√(ħ/mω)=1.

(a) Normalize this state.

(b) Plot the probability density |Ψ[x,0]|

(c) Construct the first 5 coefficients c

(d) Construct expressions for the solution to the TDSE, Ψ(x,t) and Ψ

Hint: Don't try doing this by hand but instead take a look at EX2.3.2.NB.

"I turn with terror and horror from this lamentable scourge of continuous functions with no derivatives."

--- Charles Hermite (1822–1901)