Winter 2013 Chem 356: Introductory Quantum Mechanics

Introduction to Quantum Mechanics: Syllabus 2

Introduction to Quantum Mechanics: Syllabus ............................................................................................ 2

Introduction and History ............................................................................................................................... 3

Introduction to Quantum Mechanics ....................................................................................................... 3

Historical Background ............................................................................................................................... 4

A little digression on relativity theory ....................................................................................................... 5

Introduction to Quantum Mechanics: Syllabus

Lectures: M W F 12:30 – 1:20 PHY 313

Tutorials: Friday 1:30 – 2:20 RCH 306

Website: science.uwaterloo.ca/~nooijen

Grading: 20% Assignments (Biweekly)

30% Midterm

50% Final Exam

Book: Quantum Chemistry 2nd Ed. By Donald A. McQuarrie

ISBN: 978-1-8913890-50-4

Problems and Solutions for McQuarrie’s Quantum Chemistry 2nd Ed. By Helen O.

Leung, Mark D. Marshall

ISBN: 9781891389528

*Lecture notes, to be provided

Some Fridays, we will do MathCad sessions and use computers to solve problems

For Midterm and Exam: you may bring a summary sheet (must write yourself however)

Website: To be enabled

Lectures will focus on concepts, this can be somewhat abstract

Tutorials: You ask questions

Solving Problems (sometimes extended problems): digest material, learn by practice

Winter 2013 Chem 356: Introductory Quantum Mechanics

Introduction and History 3

Introduction and History

Introduction to Quantum Mechanics

Quantum Mechanics: fundamental theory of chemistry, together with statistical

mechanics (Chem 350) forms the microscopic theories of matter

Very few fundamental postulates derive all the rest. Everything we derive (correctly) should be

possible to be confirmed by experiment (Popper, a philosopher of science).

Today: Quantum Chemistry programs (eg. Gaussian) are very powerful tools to obtain

- Molecular structure

- Spectroscopic data, IR, NMR, CD, UV-vis, Resonance Raman

- Thermochemical data H, G, S

Combine with molecular simulations

- Properties of liquids

- G for complicated reactions

- Kinetics, reaction rates

In quantum mechanics, the equations are simple, BUT hard to solve

Huge effort to develop software that can solve equations efficiently

To be expected:

Simple equation “H = E ” describes bewildering set of microscopic phenomena

The concepts underlying Quantum Mechanics are strange, puzzling, even today

So how do we deal with and study, “simple equations”, “difficult solutions” yet “funny

concepts”?

→ study model problems:

- ‘easy’ solution

- Insight into solution

- Phenomenological rule

Quantum Mechanics is old by now, started seriously in 1926

Winter 2013 Chem 356: Introductory Quantum Mechanics

Introduction and History 4

Current Frontiers / Applications include

Quantum Computing (exploiting the weirdness)

Nanotechnology : Make materials that start to ‘use’ quantum mechanics

Solid state devices (computer hardware, based on quantum mechanics)

Lasers (quantum properties of light

Our focus will be Quantum Mechanics as the fundamental theory of chemistry.

Historical Background

(Classical) Physics around 1900

- Newtonian mechanics, Hamilton/Lagrange formations

- Maxwell equations, optics, electron magnetism

- Thermodynamics:

o Heat, work, energy, entropy

- Statistical Mechanics

o Boltzmann/Gibbs

Power of theoretical description: Derive equations from the fundamental theory. Predicted

phenomena should be verified experimentally and conversely

Any (reproducible) experimental fact that does not fit the theory is a disaster, and

theory would not be universally valid; would need a change….

→ But in practice our theories (fairly simple, really) work very well (so far so good)

In 1900, most people thought everything is understood, just dotting the I’s, as far as theory

goes

Things that did not fall into place

a. Velocity of light is constant

b. Gravitational mass = inertial mass

special and general theory of relativity (Einstein)

c. Black body radiation (Planck)

Winter 2013 Chem 356: Introductory Quantum Mechanics

Introduction and History 5

d. Specific heat of solids (Einstein)

e. Photoelectric effect (Einstein)

f. Atomic spectra (Bohr)

..understanding chemistry!

Quantum mechanics!

Other new phenomena

a. X-rays (Roentgen)

b. Radioactivity (Becquerel, Curie)

c. Super-conductivity, Super-fluidity (Kamerling Onnes)

d. Discovery of electron 1898 (Thompson), nucleus 1911 (Rutherford)

Something MORE than just ‘dotting the i’s’!!

A little digression on relativity theory

(A prime example of logical thought)

Situation:

Go back to kids time, you are biking to the soccer field and throw a ball in the air with

both hands. (no hands to steer!)

Do you:

Throw the ball slightly forward (anticipating where you will be)?

OR

Throw the ball straight up as if you were not cycling as all?

OR

Throw the ball backwards?

What is the answer?

Let’s change the question.

You are in a steady moving train. How do you throw?

You are running. How do you throw?

Answer: We should throw straight up. WHY?

Winter 2013 Chem 356: Introductory Quantum Mechanics

Introduction and History 6

Because the ball already has the velocity in the forward direction, we should throw straight up.

Let’s Draw a Picture

If you toss a bottle from a moving car, it will fly with huge velocity (of the car). Velocity

depends on perspective….But…

this is not true for light!

→ the velocity of light is vacuum is constant, independent of perspective.

What does this mean? Before we can answer this, let us consider the ball a bit

more.

Question: if the boy on the bicycle, and the on the ground, measure the time of flight, do they

get equal answers? Yes.

Questions & Answers regarding ball on train (slow)

From the boy on bicycle/train perspective:

the distance travelled by the ball, 2h

the (average) velocity of the ball, yv

time of flight, t

From the ground’s perspective:

Winter 2013 Chem 356: Introductory Quantum Mechanics

Introduction and History 7

distance travelled is longer 2 xh t v

the (average) velocity of the ball, 2 2

y xv v

time: the same t

Angle of throwing the ball:

o Straight from biking perspective

o Angled from ground perspective

Now shine a flashlight to a (far away) mirror, on a moving train

Speed of light is c always

( )l l

tc

Observation: My own light (standing still) bounces back quicker than light on moving train.

For the same reason: boy (on train) says his light has returned before mine!

*note:

Winter 2013 Chem 356: Introductory Quantum Mechanics

Introduction and History 8

It would also take some time to observe the distant event. This can be taken into

account and corrected for. The math involved is a bit involved, no need for our purpose.

It is a consequence of the constancy of light that time is not absolute. Like distance which

depends on perspective, time duration also depends on perspective.

The detailed equations of special relativity are not so hard to derive.

The consequences are hard to accept, and it is pretty hard to get an intuitive feel for it.

Another consequence/Example.

c = signal velocity (eg. Velocity of mail)

→ For regular mail: world traveler sends postcards from Honolulu, New York, Tokyo: they

might all arrive at the same time

Compare receiving 3 phone calls from the same person at the same time: One from Honolulu,

one from New York, one from Tokyo

Cannot happen because we cannot travel faster than the speed of light c .