1. Announcements HW10 due today Reading: Gregory, Chapter 25, pp. 524-end Also note next week’s reading! - Gregory, Chapter 27, to p. 576, pp. 581 to end - Erazim Kohak, “A Philosophy of Personalism” (coursepack) - Steven Weinberg, “The more comprehensible the universe is the more pointless it seems” (online) Online evaluations open Final Exam Monday, April 27, 7:30am - 9:30am, In-class NPB 1002

2. Final exam  Monday, April 27, 7:30am - 9:30am, in class NPB 1002, aka here Comprehensive: covers entire course but with emphasis on material since midterm Bring: ID, scratch paper (no calculator necessary). One “cheat sheet” with formulas allowed, handwritten front and back of 1 page  Format: 30% mult. choice 40% short answer 30% essay (choice of 2)  Review session 2 nd part of class Tues next week, + during reading week TBA

3. Brief summary of general relativity: - Accelerated motion in the absence of gravity is equivalent to unaccelerated motion in the presence of gravity -Mass curves spacetime around it, leads to bending of light, which follows a geodesic shortest path on curved surface between two points. Last Time Eddington expt 1919:

4. 1. Age of Realism of late 19th century gave rise to fundamental challenges 2. Just as challenges associated with the ether resulted in the revolutionary ideas of Einstein’s special and general relativity, so challenges associated with the distribution of radiation energy gave rise to a second revolution in physics at the beginning of the 20th century. 3. Data on glowing bodies inconsistent with Jeans theory: (vibrating electrical charges) predicted at the high frequency end – the “ultraviolet catastrophe” 4.Max Planck came up with a curve that described the experimental data, but he had no idea why it worked. Planck divided the energy into finite pieces, something he was inclined not to do. Each piece was assigned energy E=hf (h=“Planck’s const.”) 5. This implied unexpectedly that energy was radiated (or absorbed) in pieces, not continuously. 6. This allowed Planck to rescue the model from the ultraviolet catastrophe and also proved helpful to Einstein in his explanation of the photoelectric effect Last Time

5. Planck’s explanation of the radiation of glowing bodies was important because 1. its hypothesis of energy quanta led Einstein to his explanation of the photoelectric effect 2. it explained why experimental data for high frequency radiation decreased instead of increasing without limit as the classical resonator model suggested 3. the quantization of energy was a fundamental departure from classical assumptions 4. it provided a universal curve for the radiation emitted by all glowing bodies depending only on their temperature 5. all of the above

6. Review: Photoelectric Effect Experiment shows: -The current is constant for a given voltage V. -The current increases with light intensity. -No current unless frequency high enough -max KE of electrons independent of intensity Shine light on metal, knock electrons out!

7. Can we understand this? Predictions of the Wave Model: -For high enough intensity, any wavelength of light should produce the photoelectric effect. -The maximum kinetic energy of the photoelectrons should scale with light intensity. -The maximum kinetic energy should be independent of the frequency. -The photoelectrons need a measurable amount of time to gain enough energy to be ejected. Not what we see.

8. Einstein’s Explanation The Photon Model (Planck) correctly predicts what’s happening. is work function of metal: energy necessary to remove one electron from surface is Planck’s const., known from radiation experiments h “photon” electron photon energy maximum electron KE

9. Atomic Spectra

10. Balmer Series Predicts the visible emission wavelengths of Hydrogen. IR and UV wavelengths are predicted by very similar rules. strictly empirical formula invented by high school teacher -- where does it come from?

11. Neils Bohr Prof. U. Copenhagen until 2 nd WW During war worked on atomic bomb in England, but argued for peaceful uses of atomic energy Invention of Bohr model of atom assuming quantized orbits for electrons Debates with Einstein on meaning of quantm theory

12. The Bohr Model of the Hydrogen Atom 1913 electrostatic PE E = ½ mv 2 -ke 2 /r electron KE Bohr noticed that Planck’s h has units of angular momentum aaaaaaa L = mvr So he assumed L = nh/2  electron wave

13. Predicted Energy Levels

14. Louis-Victor de Broglie Won the Nobel Prize in Physics in 1929 (for his 3-page PhD thesis 1924!) Professor at University of Paris Elected a member of the French Academy of Sciences 1933 Broglie stated that all matter has a wave-like nature Any moving particle or object had an associated wave Created a new field in physics, called wave mechanics, uniting the physics of light and matter

15. de Broglie’s Equation λ= particle's wavelength h= Planck's constant p= the particle's momentum p=mv electron wave

16. Erwin Schrödinger First paper has been universally celebrated as one of the most important achievements of the twentieth century, and created a revolution in quantum mechanics, and indeed of all physics and chemistry Nobel Prize 1933 Schrödinger’s Cat Thought Experiment - 1935

17. Erwin Schrödinger In 1926, at the University of Zurich, published a series of 4 papers –Wave Mechanics & Schrodinger’s Equation –Compared his approaches to Werner Heisenberg (alternate “matrix mechanics”) –Showed how to work with time-dependent phenomena

18. Schrödinger’s Equation i is the  –1 Planck’s constant divided by 2π Derivative with respect to time ψ(t) = Wave Function H(t) = Quantum “Hamiltonian” (energy of system) Max Born : ψ(x) is to be interpreted as the probability of finding a particle at position x

19. Werner Heisenberg Won Nobel Prize in 1932 in Physics "for the creation of quantum mechanics, the application of which has, inter alia, led to the discovery of the allotropic forms of hydrogen". Heisenberg pointed out that it is impossible to know both the exact position and the exact momentum of an object at the same time. Applying this concept to the electron we realize that in order to get a fix on an electron's position at any time, we would alter its momentum. Any attempt to study the velocity of an electron will alter its position. This concept, called the Heisenberg Uncertainty principle, effectively destroys the idea of electrons traveling around in neat orbits. Any electron that is subjected to photons will have its momentum and position affected.

21. l Bullets always come in "lumps" -- identical size, mass particles. l No interference: probability to arrive at screen is sum of probability to go through slit 1 and probability to go through slit 2, smooth distribution. 2-slit experiments with bullets (classical particles)

22. Intensity of water waves proportional to height Intensity of waves reaching detector through slit 2 when slit 1 is closed is smooth, and vice versa. When two waves are allowed to pass through 1 and 2 at same time, interference pattern is created. 2-slit experiments with water (classical waves)

23. l Interference pattern observed by detector at screen 2-slit experiments with electrons (do they behave like bullets or waves?)

24. Wait--we can slow gun down so that only 1 electron per hour goes through. Then we expect electron goes through slit 1 or 2, right? Every hour we get a new spot on the screen. Interference pattern builds up slowly: So--electrons are waves? So: electrons are "particle-waves"! They exhibit properties of classical waves and particles

25. Observing which slit electrons go through I) Wait a minute: if electrons can be seen to go through one slit or the other, how can they interfere with themselves? Let's try to determine which slit they pass through with a "camera" Act of measurement destroys interference pattern!

26. Weaken laser beam so that very few photons come out! 2-slit experiments with light Light is "particle-wave" just like electrons! (except photons move at speed of light, have no mass)

27. Act of observation destroys interference pattern! One way to say this: pinning down particle's position made momentum indeterminate! Heisenberg uncertainty principle: uncertainty in your measurement of particle’s position Uncertainty in measurement of particle’s momentum Planck’s const. divided by 2  Planck’s const/2 