1
NAME_KEY_
Answer all question providing your reasoning in order to earn partial credit. The exam total
is 150 points.
Energy of interaction of an electron with the B field (assume for electron g-factor
(
)
The energy of interaction between magnetic mome
Heisenberg uncertainty principle
It is impossible to specify simultaneously, with arbitrary precision, both the momentum and the position of a particle.
Consider the free particle, (x) = Aeikx is an eigenfunction of the momentum
operator with eigenvalue =
The principles of quantum theory
Topic 7C
September 5, 2016
Overview
Extract information from the wavefunction by determining eigenvalues and expectation values of Hermitian operators.
Understand wavefunction shape in terms of the potential.
Formalize
Dynamics of microscopic systems
Topic 7B
August 31, 2016
Overview
Quantum theory is the framework we need to understand the properties of atoms
and molecules
Procedures to determine and interpret the wavefunction
Restrictions on the form of the wavefun
Background: Classical Mechanics and Waves
Foundations B,C
August 29, 2016
Overview
The quantization of energy is a central theme of physical chemistry.
While the theoretical methods applicable to quantum systems are different than
classical methods, the
Quantum theory of translation
Topic 8A
September 12, 2016
Overview
item
CHM 341 | Topic 8A
2/17
A free particle undergoes translation
Schrdinger equation for a particle free to move in one dimension:
2 d2
h
(x) = E(x)
2m dx2
We know the solutions are:
k
Vibrational motion
Topic 8B
September 16, 2016
Overview
Today
Quantum approach to vibrational motion from the harmonic oscillator model
Wavefunctions are products of gaussians and Hermite polynomials
Energy levels are evenly spaced
CHM 341 | Topic 8B
2
Title
Topic 9B
October 5, 2016
Overview
Electron spin
CHM 341 | Topic 9B
2/27
More than one electron
The potential of one electron in an atom V (r) = Ze2 /40 r describes the
Coulombic attraction between the electron and nucleus and allows us to write:
n,
The origins of quantum mechanics
Chapter 7A
August 30, 2016
Overview
Experimental results that motivated the development of quantum theory
Introduction to spectroscopy
Evidence for the dual, wave-particle nature of quantum systems
Unlike classical par
Hydrogenic Atoms
Topic 9A
September 29, 2016
Overview
This chapter:
"Atomic electronic structure" describes the distribution of electrons around atoms,
usually in terms of occupation of orbitals
Electron spin and its impact on energy levels and spectra
Hydrogenic Atoms
Topic 9A
September 29, 2016
Overview
This chapter:
"Atomic electronic structure" describes the distribution of electrons around atoms,
usually in terms of occupation of orbitals
Electron spin and its impact on energy levels and spectra
Homework
1. Exercise 9A.7(a) - radial distribution function
2. Exercise 9A.9(b) - orbital labels, angular momentum
3. Problem 9A.2 (a) - orbital orthogonality
4. Problem 9A.3 (c) - mean radius of an electron
CHM 341 | Topic 9A
20/20
Topic 8C - Rotational motion
Reading
8C.1
8C.2
Outline
1. Particle on a ring
2. Quantization of angular momentum, a qualitative approach
3. Solutions to the Schrdinger equation
4. Angular momentum
5. Particle on a sphere
6. Solutions to the Schrdinger equ
Topic - 9B
Reading
9B.1
9B.2 (a)
9B.3
Outline
1. The orbital approximation
2. Electron spin and the Pauli principle
3. Nuclear shielding
4. The Aufbau principle
5. Hunds rules
6. Self-consistent field orbitals
The orbital approximation
More than one elect
Quantum theory of motion - Translation
Reading
8A.1
8A.2
8A.3
Tunneling, section 8A.4, will be covered at the end of the chapter time permitting.
Outline
1. Particle in a box
2. Solutions from boundary conditions
3. Energy levels
4. Characterization of pa
Quantum theory of motion - Translation
Reading
8A.1
8A.2
8A.3
Tunneling, section 8A.4, will be covered at the end of the chapter time permitting.
Outline
1. Particle in a box
2. Solutions from boundary conditions
3. Energy levels
4. Characterization of pa
Topic 8B - Vibrational Motion
Reading
8B.1
8B.2 (a)
Outline
1. Harmonic oscillator
2. Energy levels
3. Eigenfunctions
4. Probability densities and expectation values
A harmonic oscillator
An oscillator undergoes harmonic motion if it experiences a restori
Topic 8C - Rotational motion
Reading
8C.1
8C.2
Outline
1. Particle on a ring
2. Quantization of angular momentum, a qualitative approach
3. Solutions to the Schrdinger equation
4. Angular momentum
5. Particle on a sphere
6. Solutions to the Schrdinger equ
Topic 8B - Vibrational Motion
Reading
8B.1
8B.2 (a)
Outline
1. Harmonic oscillator
2. Energy levels
3. Eigenfunctions
4. Probability densities and expectation values
A harmonic oscillator
An oscillator undergoes harmonic motion if it experiences a restori
CHM 341 - Physical Chemistry: Molecular Structure, Bonding, and Dynamics
Prof. Heather Jaeger, [email protected]
M W F 11:10-12:00, Packard Lab 466
Description
This course presents the quantum behavior of chemical properties and the corresponding developm
1
NAME_KEY_
Answer all question providing your reasoning in order to earn partial credit. The exam total
is 80 points.
TOTAL_
2
1. (20) Either answer the question asked or circle the best answer. 5 pts. ea.
a. An eigenfunction of the momentum operator
i.
Problem Set 4
Problem 1. SAB 10.15, page 392.
The spin part of the wavefunctions for the first excited state of helium are = (1) (2),
= (1) (2) + (1) (2), and = (1) (2). Since = , what are the values for
the three wavefunctions?
= 1 + 2
Since for the tw