separation of the observer from the Heisenberg may have slept here. Anonymous PHY100S (K. Strong) - Lecture 20 - Slide 1
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1 separation of the observer from the phenomenon to be observed is no longer possible. Werner Heisenberg, German physicist ( ) 1976) Heisenberg may have slept here. Anonymous PHY100S (K. Strong) - Lecture 20 - Slide 1
2 Current Assignments... For today Read Sections 12.7, 13.1 Office hours: For Lecture Tuesdays Read Sections & Thursdays Homework #4 Posted March 7. Due 11:00 AM, Friday, March 22 Homework #5 Handed d out today. Due 1100AM 11:00 AM, Fid Friday, April il5 Writing Assignment #2 Posted Feb. 28. Due 11:00 AM, Thursday, April 4 Suggested Conceptual Exercises Chapter 13: 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33 Tutorial #9 Homework #3 will be returned PHY100S (K. Strong) - Lecture 20 - Slide 2
3 PHY100S (K. Strong) - Lecture 20 - Slide 3
4 Review of Lecture 19 Textbook, Chapter 12 The quantization of light The quantum theory of radiation Matter waves, matter fields The quantum theory of matter [ Quantum nonlocality and uncertainty ] PHY100S (K. Strong) - Lecture 20 - Slide 4
5 Plan for Lecture 20 Textbook, Sections The quantum theory of matter Quantum nonlocality and uncertainty Textbook, Section 13.1 The Uncertainty Principle PHY100S (K. Strong) - Lecture 20 - Slide 5
6 L19: The Wave Theory of Matter Every material particle has wave properties with a wavelength equal to h/mv, where m is the particle s mass and v is its velocity. = h/mv PHY100S (K. Strong) - Lecture 20 - Slide 6
7 How do we know that matter has wave properties? Textbook Figure 12.8 Voted #1 in a 2002 poll of the most beautiful experiments in physics by Physics World magazine. The double slit experiment can be done with electrons. PHY100S (K. Strong) - Lecture 20 - Slide 7
8 Electron Double Slit Animations Detailed description of both versions of the double slit experiment est/harrison/doubleslit/doubleslit.html Results for the electrons utoronto ca/generalinter est/harrison/doubleslit/flash/histogram.html Results for waves and particles est/harrison/doubleslit/flash/doubleslit.htmlhtml PHY100S (K. Strong) - Lecture 20 - Slide 8
9 Electron Double Slit - Results The result is an wave interference pattern, like that produced by photons. The interference pattern also builds up spot by spot, showing that matter is made of particles. Movie of the experiment produced by Hitachi Ltd: hitachi co e/doubleslite-n.wmv Textbook Figure 12.9 Textbook Figure PHY100S (K. Strong) - Lecture 20 - Slide 9
10 The Quantum Theory of Matter A new type of field called a matter field exists in nature. Like EM fields, matter fields are quantized. For example, the matter field for electrons is allowed to possess enough energy for either 0 electrons, or 1 electron, or 2 electrons, and so on. Electrons (and other material particles) exist because matter fields are quantized in just these energy increments. PHY100S (K. Strong) - Lecture 20 - Slide 10
11 Visualizing the Double Slit Experiment for a Single Electron Textbook Figure The matter field moves through the two slits, and collapses into a single electron when it hits the screen. PHY100S (K. Strong) - Lecture 20 - Slide 11
12 How is an electron similar to a photon? (A) Both have electric charge. (B) Both have mass. (C) Both move at lightspeed. (D) Both hit a tiny point on a viewing screen in the double slit experiment. (E) Both are quanta. PHY100S (K. Strong) - Lecture 20 - Slide 12
13 Quantum Nonlocality Key ideas of quantum physics Quantization of the EM field Existence of the matter field Quantization of the matter field The nonlocal collapse of the quantized EM or matter field to an uncertain small point of interaction This is called quantum nonlocality PHY100S (K. Strong) - Lecture 20 - Slide 13
14 Quantum Uncertainty The electron pattern on the screen builds up point by point, but is there any way to tell exactly where any particular electron is going? No, there is not! With identical electrons and identical preparations, we get different results. This is unprecedented in Newtonian physics, and is the core of the difference between the quantum world and the deterministic Newtonian one. PHY100S (K. Strong) - Lecture 20 - Slide 14
15 Quantum Uncertainty Textbook Figure Although the location of any individual electron impact is impossible to predict, the overall pattern is well defined. PHY100S (K. Strong) - Lecture 20 - Slide 15
16 Probability The pattern is a pattern of probabilities: The intensity of the matter field at any point represents the probability that an electron will hit the screen at that point. But this is not a probability like a coin toss, which appears random because we don t know the initial conditions precisely; this is an innate probability. There is nothing more we could know about the electron that would help us predict where it will go. PHY100S (K. Strong) - Lecture 20 - Slide 16
17 Schroedinger s Equation Matter waves are predictable because of the predictability of the statistical patterns. Schroedinger Equation describes the motion of the matter wave for any material particles. It correctly describes experimental results such as the double slit experiment with electrons. It can also be applied to electrons in atoms Chapter 13 PHY100S (K. Strong) - Lecture 20 - Slide 17
18 How does quantum uncertainty differ from the uncertainty involved in a coin flip? (A) With sufficient information, quantum uncertainties can be removed, but no amount of information can make a coin flip's outcome predictable. (B) With sufficient information, a coin flip's outcome can be predicted, but no amount of information can remove quantum uncertainties. (C) They don't differ in any essential way--with sufficient information, both types of uncertainty can be removed. (D) They don't differ in any essential way--no amount of information can remove either type of uncertainty. PHY100S (K. Strong) - Lecture 20 - Slide 18
19 Quantifying Quantum Uncertainty Consider a quantized matter field containing enough energy for just one electron, moving through empty space along the x-axis. The intensity of the matter field at any point represents the probability bilit that t an electron will be found at that point. The matter field is spread out in space and has a wavelike character as shown in the figure. Textbook Figure 13.2 PHY100S (K. Strong) - Lecture 20 - Slide 19
20 Quantifying Quantum Uncertainty The wave representing a single particle whose uncertainty in position is x, moving along the x- axis. It is a wave spread out over a limited distance. We need a way of representing the matter field for a single particle wave packet This shows that the electron does not have a precise position or a precise wavelength. Textbook Figure 13.2 PHY100S (K. Strong) - Lecture 20 - Slide 20
21 Position & Velocity of Wave Packets x = uncertainty in position v = uncertainty in velocity What happens to if we decrease x? decreases What happens to v if we decrease x? = h/mv, so v = h/m shorter means larger velocity and also means a larger uncertainty in velocity, v PHY100S (K. Strong) - Lecture 20 - Slide 21
22 Position & Velocity of a Wave Packet Textbook Figure x of packet A > x of packet B of packet A > of packet B v of packet A < v of packet B PHY100S (K. Strong) - Lecture 20 - Slide 22
23 The Uncertainty Principle In 1927, Werner Heisenberg showed that the product of x and v was constant. The position and velocity of every material particle are uncertain. Although either uncertainty can take on any value, the two are related by the fact that their product must approximately equal Planck s constant divided by the particle s mass. In symbols, ( x) ( v) h/m where h is Planck s constant and m is the particle s mass. PHY100S (K. Strong) - Lecture 20 - Slide 23
24 Uncertainty in Position Textbook Figure 13.4 & Velocity x and v have a range of possibilities, but if one is small the other must be large. PHY100S (K. Strong) - Lecture 20 - Slide 24
25 Relevance of the Uncertainty Principle Because h is so small, uncertainties in x and v are relevant only for subatomic particles. The Uncertainty Principle means that no object can ever be truly motionless. Textbook Figure 13.5 If x issmall, v must be large and so v will also be large. Significant effects in the quantum world. PHY100S (K. Strong) - Lecture 20 - Slide 25
26 Concept Check 3 A particle having a very precise velocity has a wave packet that: (A) occupies a wide region of the x-axis (B) occupies a narrow region of the x-axis (C) moves with a wide range of velocities (D) moves with a narrow range of velocities PHY100S (K. Strong) - Lecture 20 - Slide 26
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