Lecture 2: The Special Theory of Relativity I
Michelson-Morley Experiment Einstein's postulates of special relativity
1
Classical Relativity: Example
v L A stick length of L is moving with constant speed v along the positive x axis as observed i
Physics 237 Solution to Homework Assignment #1 1-8. (a) This will not yield the same result since distance measured depends on the relative motion of the frames (Lorentz transformation). (b) As we saw in class, this will yield the same result if we d
m x 2 6-35. The wave function is given by: 0 x C0 exp . 2h m x 2 2 (a) Normalization: 0 x dx C0 2 exp dx 1 h
2
m x 2 2C0 exp dx 1 h 0 1/ 4 h m 2 2C0 1 C0 2 m h (b) 1/2 1/2 3/2 m x 2 h h m m x 2
Physics 237 Spring 2005 Solution to Homework Assignment #6
6-2. The time dependent Schrodinger equation is: h2 2 ih V . 2m x 2 t We are given: x,t Aei kx t .
h2 k 2 h2 2 Hence, we get: (a) ih h & (b) V V . 2 2m t 2m x In both (
Physics 237 Solution to Homework Assignment #4 4-3. The Lyman series corresponds to wavelengths given by the formula: 1 1 = R 1 2 ;n = 2, 3, 4,. . For _ = 164.1 nm, n = 1.5. So, the observed line is not in n the Lyman series. 4.6. This uses Ruth
Physics 237 Spring 2005 Solution to Homework Assignment #3 3-14.
1 . By definition, u() d gives the energy density # hc & exp % )1 $ !kT ( ' d! in the wavelength interval (, +d). Hence, u ( ! )d! = u ( f )df " u ( f ) = u ( ! ) . df This then yields
Phys 237/237H: Introduction to Modern Physics
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Summary of Lecture 2
Michelson-Morley Experiment: speed of light is independent of reference frame - no "ether" Einstein's postulates of special relativity:
Principle of relativity: no absolute reference frame Principle of constancy: speed of lig
Summary of Lecture 3
Spacetime diagrams Lorentz contraction: "an object in motion contracts in the direction relative motion" LPROPER
L' =
Time dilation: "A moving clock slows down"
T ' = TPROPER
Relative velocity transformation:
The space
Basic idea of a laser: Exploit positive feedback inherent in stimulated emission: Photon + Excited atom (B) ! Two photons + ground state atom (A) This could lead to "lasing": an avalanche of photons at the selected frequency: "= #E/ !
B A
Problem: