Class 15, 2/26/04
Highlights:
* Quick overview of preview of this class, and Class 14
* R1: Particle/wave property of light
** Energy of a photon
E = h x frequency
(neu), as was put forward by Planck in 1900.
** Momentum of a photon
p = E/c = (h
x frequency)/c, as later proven by experiment;
** Next use the relation c = (frequency)
x (wave length), the momentum of the photon can be written as
p = h/ (wave
length), or (wave length) = h/p.
* N1: Particle/wave property of massive particle
** In the 1920s, de Broglie proposed that particle should
have wave properties too ! He was subsequently proven right by experiments.
Not only that, electron microscope was made based upon the wave property
of electron.
** The de Broglie equation:
(wave length
of a massive particle) = h/p, where p is the magnitude of the momentum
of a massive particle,
p = m v ~
M v , for [(v/c)^2] << 1 ( " ~ " denotes "approximately equal to";
and " << " denotes "much less.")
* N2: Electron microscope (See HW8, SA8.2)
** Converting electric potential of
a electron to its kinetic energy. The unit of electric potential energy is
denote by electron charge e and volts V,
1 eV = 1.6 x 10^-19
kg m^2 s^-2, see Appendix A of TB1.
* N.3 Our Star
** Brief history of the Sun
** How it shines; Fig. 15-7.
*** Professor Hans Bethe of Cornell
U got the Nobel Prize in 1967 for his contribution to the understanding of
star energy
** "Tag of war" between gravitational pull and nuclear
fusion energy push out ---- gravitational/fusion pressure balance or equilibrium.
*** See Fig. 15.8.
** Fusion vs fission, Fig. 15.5;
** Layers of the Sun, Fig. 15.4;
** Studying Sun by Doppler effect: Fig. 15.9.
* N.4, (back to some math)
** Pythagoras thm in Euclidean space, which our flat 3-dimensional
space is,
r^2 = x^2 + y^2
+ z^2 .
** The length-squared of a directional line (a vector),
r^2, is invariant under coordinate change. (e.g., Distance from Davis to
Manhattan does not change under coordinate change or rotation. Although,
its projections in each direction (x, y, z) changes when different coordinates
are used.
** Pythagoras thm also apply to momentum
p^2 = (p_x)^2
+ (p_y)^2 + (p_z)^2,
which also invariant under spatial
coordinate change.
** In our (3+1)-dimension spacetime, the Minkowski space,
Pythagoras thm is generalized to Minkowski thm
*** (Invariant length in Minkowski)^2
= (invariant length in 3-space)^2 - (ct)^2 = r^2 - (ct)^2, which is
invariant not only under coordinate change in space, but also time change
caused by relative constant motion.
*** Similarly Minkowski thm also apply
to momentum-energy, i.e.,
p^2 - (E/c)^2 = an invariant under coordinate change in spacetime, due
to rotation or relative constant motion.
Bonus challenge:
A simple calculation will reveal this invariant quantity. This is a bonus
challenge to student. Whoever first derives this result and e-mail to Professor
Chau will get 1.0 bonus.
****** Below was posted before the class. *****************
Reminder:
* Look forward to receiving your answers to "Questionnaires after Quiz 2"
before Thursday, 2/26/03, midnight. Please keep the Subject of the e-mail
as is.
* Quiz 2 & HW6 rebuttal due next Tuesday. Please follow the procedure
of sending Professor Chau an e-mail first (please remember to put in
Subject "10B; Rebuttal xxx.") and give her the full graded set (either sliding
under her office door or handing to her right after the class.).
Announcement:
* Please see revised Reading Assignments on the web.
* In view of the coming Quiz 3, Thursday, 3/4/04, next week, the immediate
reading assignment is less than usual, as listed below.
Week-8 (2/26-3/4 )
TB1:
· Partial Our Star;
Read p.496-508 & summary pages (i.e., 15.1 to 15.3 and summary pages
of TB1).
· Fig. 7.20 on p.186 and its
explanations; Fig. 11.8 on p. 304 and its explanations.
TB2:
· Pp.263-p.282, Chpt 11
of TB2.
Preview of class:
* Wave property of particles with mass;
* More about uncertainty relations in Quantum Mechanics;
* Starting new chapters listed above.
Sigu-up items:
Sign-up item, Class
15, 2/26/04
(1) Initial.