Chem 3890 Assignment 1
1. Ordinary derivatives
X[x_] := B * Sin[n * Pi * x / l]
(a) Take the difference
deltaX = X[x2] - X[x1]
- B Sin
+ B Sin
(b) Use the derivative
dX = (D[X[x], x] /. x x1) * (x2 - x1)
Chem 3890 Assignment 5
1. Numerical solution of the SE for the HO at and near the ground-state energy.
(i) Schrdinger equation for HO with dimensionless coordinate at the ground state energy. Here is
related to x in Eq. 2.71 of Griffiths, and the Schrding
Chem 3890 HW 7
1. Average potential and kinetic energy for a 1s electron
See handwritten sheet for details.
Vbar = - 8 * I1 * Integrate[ * Exp[- 2 * ], cfw_, 0, Infinity]
- 2 I1
See handwritten work.
Each radial function should be multiplied by
[m*omega/hbar]^cfw_3/2 to have the correct units of
1. 3D particle-on-a-spring-see handwritten pages
(iii) Some derivatives
Fnl = A * ^ cfw_n * Exp[- ^ cfw_2 / 2
Chem 3890 Assignment 6
1. Particle-in-a-bowl solved by oscillating the pup
(i) SE in dimensionless variables-see handwritten page
(ii) Plot harmonic and anharmonic potential energies
PE made dimensionless by dividing by
VHO = ^ cfw_2 / 2
Chem 3890 Assignment 4
1. Uncertainty relation for x and K. See handwritten sheet.
2. Check result from Q1 for a particular case
$Assumptions = cfw_b > 0, k > 0, > 0, m > 0
cfw_b > 0, k > 0, > 0, m > 0
Chem 3890 HW0
Clear variable values each time the .nb is run.
Question from Getting Started
How many distinct variables in
ab + a*b + cosa +Log[a*b] +Exp[a] + sin(ab) ?
The distinct variables are ab, a, b, cosa, and sin, so 5. No
Chem 3890 HW3
1. Orthogonal polynomials
0 = A0;
1 = A1 * x;
3 = A3 * (x ^ 3 - B1 * x);
We know that each of these functions is normalized and that each distinct pair is orthogonal. This gives
in principle six equations for 4 unknow