Chemistry 2500
The Particle-in-a-Box
1
The Particle in a box (or 1-D well)
The first, and possibly simplest, problem to which we
apply the Schrdinger Equation is:
The Particle-In-A-Box (PIAB) problem
- a.k.a. Particle in a 1-dimensional well
For the PIA
Topic D:
PIAB Energy Expression and
Wavefunctions
Chemistry 2500H
1
The energy level expression - PIAB
Now that we have solved the PIAB problem, we
can learn from the answers:
PIAB wavefunctions:
PIAB energies:
n
L
(x) A sin
n2h2
En
8mL2
x n 1, 2,
Mastering Chemistry (MC2500HKING)
Student Purchasing Options
1. Textbook packaged with MasteringChemistry- ISBN: 9780321766205
(has been ordered by the bookstore and will be in later this week)
2. Mastering with eText standalone
3. Mastering without eText
What can we do with our knowledge
of the wave-particle duality?
Some calculations
1
Calculating the number of photons:
Electromagnetic radiation with a specific frequency is
observed possessing energies that increase only in
increments of nh
How many pho
Topic E:
The Wavefunction, Probability, and
Normalization
Chemistry 2500H
1
Notes on derivatives
CHEM 2500H
Operators work from right to left:
2 d 3
2
2
4
3x
x 3x 3x 9 x
dx
Operator says to take
the first derivative with
respect to x AND THEN
multiply t