PHYS 343 – Wave Mechanics

Instructor - Mark BoulayOffice 208C Stirling Hallmark.boulay@queensu.ca

Office hours for PHYS 343 – Wednesday 1:00-3:30

Lectures are T 12:30-1:30 Th 11:30-12:30 Fr 1:30-2:30

Course web site http://www.physics.queensu.ca/~phys343/

Lecture notes, assignments, and solutions will be posted to course web site

Course mark breakdown:

Assignments 30%Mid-term 20%Final exam 50%

Exams are closed book, no notesformula and constants sheet will be provided

Note on assignments:

Total of 10 assignments out on Fridays (starting next week),due at the start of following Friday lecture (1:30 PM)

Please hand assignments in on time,

assignments and solution sets will be posted to the course website

Assignments WILL NOT be accepted after solutions have been posted!

Course text

“Modern Physics” Serway, Moses and Moyer 3rd edition

Additional texts

“Introduction to the Structure of Matter – A Course in Modern Physics”Brehm and Mullin 1989 – more advanced but good reference

“Introduction to Quantum Mechanics”Griffiths – Many solved problems

Quantum Mechanics texts in Stacks (QC 174.12, QC 21.2)

Course Overview – PHYS 343

Part of the series 242/342 – 343 – 424 that can loosely be called “Modern Physics”:

Fundamental change to mechanics brought on by experimental results of the late 19th and early 20th centuries

In addition to Newtonian mechanics

Matter possesses wave characteristics.

Originally motivated by (Louie de Broglie 1924 doctoral thesis) similarity between quantizedstates and standing waves. Energy quantization was associated with discretely allowedconfiguration in a quantum system; comparable to harmonic frequencies for discrete modes ina vibrating medium

Also motivated by symmetry with the quantum properties of EM radiation (which was treatedas both particle & wave, with conclusive verification by A. Compton in 1923)

2

2

dtxdmFrr

=

The matter-wave hypothesis assigns a wavelength λ to a particle with momentum p

and f = E/hh = Planck’s constant

The wave aspect becomes significant when the characteristic wave dimension approaches that of the dynamical system

Incorporating this new aspect has been done (not surprisingly) in more than one way. Our study of modern physics begins with the specific approach of

Wave Mechanics to the more general topic of Quantum Mechanics

In PHYS 343 We will cover

• (primarily) foundations of Wave and Quantum Mechanics and • some applications to physical systems

ph

= λ

PHYS 343 - Course Outline

1. Introduction and Review of Waves2. Postulates of Quantum Mechanics3. Schrödinger Equation and the 1-D Infinite Well4. 1-D Finite Well5. Step and Barrier Potential 6. Harmonic Oscillator7. Central Force and Angular Momentum8. The Hydrogen Atom9. Spin10. Multi-electron Atoms11. Molecules and bonds12. Quantum Statistics

Note that the 2nd order differential equation governing Newtonian Mechanics

with 2 initial conditions

is deterministic: particle trajectory is precisely determined

In our treatment, determination of the wave function replaces theproblem of solving for

We will see that the quantum particle now has a probabilistic detectability.

2

2

dtxdmFrr

=

0t|)dtxd and x( =

rr

(t)xr

(t)xr

t),xr(Ψ

(t)xr(t)xr

2

2

dtxdmFrr

= ψδδψψ

δδ

tiV

xmh

h=+

−2

22

2

Newton’s 2nd law (N2): Schrödinger's equation

We will begin with a review of waves themselves.

In PHYS 343, we will develop tools to generate solutions to Schrödinger's equation,and then interpret particle’s physical behavior from the solution wave function.

We will find that with proper mathematics in place, the Schrödinger equation and some simple arguments based on physical symmetry and boundary conditionstell us about:

•the structure of the atom•the nature of molecular bonds•physical phenomena exist that can not be explained by N2(quantum tunneling, wave nature of matter)