Winter Physical Systems: Quantum and Modern physics

Dr. E.J. Zita, The Evergreen State College, 6.Jan.03Lab II Rm 2272, zita@evergreen.edu, 360-867-6853

Program syllabus, schedule, and details online at http://academic.evergreen.edu/curricular/physys2002/home.htm

Monday: QM (and Modern Q/A)

Tuesday: DiffEq with Math Methods and Math Seminar (workshop on WebX in CAL tomorrow at 5:00)

Wed: office hours 1:00

Thus: Modern (and QM Q/A) and Physics Seminar

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Outline:• Logistics

• Modern physics applies Quantum mechanics

• Compare Quantum to Classical

• Schroedinger equation and Planck constant

• Wave function and probability

• Exercises in probability

• Expectation values

• Uncertainty principle

• Applications… Sign up for your minilectures

Time budget

E&M DiffEq Mechanics Total time5 hrs class 5 hrs class 5 hrs class 154 hrs reading 4 hrs reading 4 hrs reading 126 hrs homework 6 hrs homework 6 hrs homework 18

46 minimum

Plus your presentations:

* minilectures (read Learning Through Discussion and ML Guidelines)

* library research (to prepare for projects in spring)

Science Seminar:

* Tues. Math seminar: Chaos and Humor

* Thus. Physics seminar: Alice and Heisenberg

Quantum Mechanics

by Griffiths

Theory : careful math and

careful reasoning

Modern Physics

by OHanian

Applications: more numerical than theoretical

Links between QM and Modern

From Tom Moore’s Unit Q

How can we describe a system and predict its evolution?

Classical mechanics: Force completely describes a system: Use F=ma = m dp/dt to find x(t) and v(t).

Quantum mechanics:

Wavefunction completely describes a QM system

Review of Modern physics basics

hcE pc

hp

Energy and momentum of light:

Can construct a differential operator for momentum (more careful derivation in a few weeks)

2

h

2k

2

2

hhp k

x

Planck constant h = 6.63 x 10-34 J.s

Invented by Planck (1900) to phenomenologically explain blackbody radiation

Planck derived h from first principles a few weeks later, treating photons as quantized in a radiating cavity

Fundamental unit of quantization, angular momentum units

Used by Einstein to explain photoelectric effect (1905) and Bohr to derive H atom model (1912)

Schroedinger eqn. = Energy conservation

E = T + V

E = T + Vwhere is the wavefunction and

energy operators depend on x, t, and momentum:

p̂ ix

E i

t

22

2i V

t x

Solve the Schroedinger eqn. to find the wavefunction, and you know *everything* possible about your QM system.

Wave function and probability

Probability that a measurement of the system will yield a result between x1 and x2 is

22

1

( , )x

x

x t dx

Measurement collapses the wave function

•This does not mean that the system was at X before the measurement - it is not meaningful to say it was localized at all before the measurement.

•Immediately after the measurement, the system is still at X.

•Time-dependent Schroedinger eqn describes evolution of after a measurement.

Exercises in probability: qualitative

Exercises in probability: quantitative

1. Probability that an individual selected at random has age=15?

2. Most probably age? 3. Median?

4. Average = expectation value of repeated measurements of many identically prepared system:

5. Average of squares of ages =

6. Standard deviation will give us uncertainty principle...

0

( )( )

j

j N jj j P j

N

2 2

0

( )( )

j

j N jj j P j

N

Exercises in probability: uncertainty

Standard deviation can be found from the deviation from the average:

But the average deviation vanishes:

So calculate the average of the square of the deviation:

Homework (p.8): show that it is valid to calculate more easily by:

1.1 Find these quantities for the exercise above.

j j j

0j

22 j

22 2j j

Expectation values

2( , )x x x t dx

Most likely outcome of a measurement of position, for a system (or particle) in state :

Most likely outcome of a measurement of position, for a system (or particle) in state :

*d xp m i dx

dt x

Uncertainty principle

Position is well-defined for a pulse with ill-defined wavelength. Spread in position measurements = x

Momentum is well-defined for a wave with precise. By its nature, a wave is not localized in space. Spread in momentum measurements = p

We will show that x p 2

Particles and Waves

Light interferes and diffracts - but so do electrons! in Ni crystal

Electrons scatter like little billiard balls - but so does light! in the photoelectric effect

Applications of Quantum mechanics

Sign up for your Minilectures

Blackbody radiation: resolve ultraviolet catastrophe, measure star temperatures

Photoelectric effect: particle detectors and signal amplifiers

Bohr atom: predict and understand spectra and energies

Structure and behavior of solids, including semiconductors

Scanning tunneling microscope

Zeeman effect: measure magnetic fields of stars from light

Electron spin: Pauli exclusion principle

Lasers, NMR, nuclear and particle physics, and much more...