FALL SEMESTER 2003

WELCOME TO CHEM 614, A COURSE ON

QUANTUM CHEMISTRY

YOUR INSTRUCTOR IS

Michael A. J. Rodgers

Office is PSLB 310

e-mail: rodgers@bgnet.bgsu.eduSend me your e-mail addresses ASAP

COURSE WEB SITE ADDRESS:

http://www.bgsu.edu/departments/chem/faculty/rodgers/quantum

There is no recommended book. “Quantum Chemistry” by Levine and “Molecular Quantum Mechanics” by Atkins are useful reference

texts.

I shall loan you a copy of a math book (Barrante) that you might find useful.

The syllabus for the course is defined by the 12 or so Modules (chapters) that you will eventually find under the “Modules” page on

the Quantum web site.

Class meets TH at 1630 in OH 132. I shall present “lectures” that are based on the content of the Modules. The Modules contain much

more material than I can cover in the lectures, so you will have to do a lot of reading on your own in order to complete the homework

assignments.

The “pace” of the course will be set by the homeworks. A homework assignment will be given every week. It is up to you to do the

homeworks.

If you complete the homework assignments assiduously you will have no surprises when the Tests come around.

SPEAKING OF TESTS, THERE WILL BE FOUR (4)

TEST 1 WILL BE ON SEPT 25 (1+ HOUR)

TEST 2 WILL BE ON OCT 21 (1+ HOUR)

TEST 3 WILL BE ON NOV 25 (1+ HOUR)

TEST 4 (THE FINAL) WILL BE HELD ON DECEMBER 16 (2 HOURS), IT WILL COVER THE WHOLE COURSE.

YOUR GRADE FOR THE COURSE WILL BE CALCULATED FROM THE POINTS YOU ACCUMULATE ON ALL 4 TESTS

POINTS FOR THE FINAL WILL BE WEIGHTED DOUBLE

MODULE 1

FROM PLANCK TO EINSTEIN TO DE BROGLIE TO SCHRÖDINGER…

You should be familiar with the major rethinking about the physics of electromagnetic radiation and matter that occurred at the opening of the 20th

century.

If not, I suggest that you read and digest an account that you will find in any advanced text on modern physics, physical chemistry, and the like.

In Module 1 you will find a very brief and hardly sufficient overview of the historical background to the birth and early growth of quantum mechanics, the

concept of wave-particle duality, and the contributions of the “greats”.

I urge you to read this historical material and to supplement it from other sources. It will help you ease into the course material.

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1: Langmuir

2: Planck

3: Mme Curie

4: Lorentz

5: Einstein

6: Debye

7: Bragg

8: Dirac

9: de Broglie

10: Born

11: Bohr

12: Schrödinger

13: Pauli

14: Heisenberg

15: Brillouin

Solvay Conference

Brussels, Belgium, 1927

As a result of his contemplation of the PHOTOELECTRIC EFFECT, Einstein proposed that when light was emitted from a source, it was not a continuous

wave, but as a beam of minute energy packets (quanta) and this was the way that it generated electrons on impinging on the sensitive metal surface.

Eventually these light quanta became known as photons.

In 1924 Louis de Broglie proposed that if light (a classical wave) can display particle-like behavior, then matter (classical particles) should likewise display

wave-like behavior under particular experimental conditions.

This proposal has brought an intriguing symmetry to natural phenomena.

de Broglie argued that the equation that Einstein had arrived at for photons, viz.

where is the wavelength, p is the momentum and h is Planck's constant, should be applicable also to matter.

On this concept, would be the wavelength of matter waves that are associated with the particle.

/h p

Consider a particle of mass m moving with velocity v.

The momentum is given by p = mv

And its de Broglie wavelength is given by = h/mv.

For masses in the kg range, moving with everyday velocities (e.g., a fast moving baseball) is of the order of 10-34 m, a value that is

not observable and of no consequence in everyday life.

However, for an electron traveling at 1% of the speed of light

~ 10-10 m, i.e. 100 pm

This is in the x-ray spectrum, and clearly measurable.

In fact, it is now commonplace that electron beams of such character can be employed for diffraction studies (a specific property of waves) to obtain information on the structure of

crystalline materials.

Thus it seems we have a paradoxical situation:

an electron shows properties of both a particle (which we think of as having a particular set of spatial coordinates, i.e. localized)

and it shows wave-like properties (in which it cannot be pinned to a particular set of coordinates).

The paradox is resolved by deciding that an electron (and electromagnetic radiation) is neither a particle nor a wave but can show properties of either (but not simultaneously both), depending

on how we carry out the observations.

So electrons and photons resemble one another but they are not twins.

electrons have rest mass and travel at any velocity less than 3x108 m s-1

photons have no rest mass and always travel at 3x108 m s-1 in vacuo.