Physics 451

1. Physics 451 Quantum mechanics I Fall 2012 Karine Chesnel

2. Homework First Homework (#1): pb 1.1, 1.2, 1.3 due Friday Aug 31st by 7pm First help sessions: Thursday Aug 30th exceptionally from 4:30pm

3. Until 20th century: Classical Newtonian Mechanics… Newton’s second Law Kinetic energy Mechanical energy of the system Introduction toQuantum mechanics Some History Deterministic view: All the parameters of one particle can be determined exactly at any given time

4. Werner Heisenberg 1901-1976 Erwin Schrödinger 1887-1961 Wolfgang Pauli 1900- 1958 Uncertainty Principle Schrödinger Equation Pauli exclusion principle Introduction toQuantum mechanics Some History Early 20th century: Some revolutionary ideas from bright minds…

5. 3) Wave-particle duality: All particles can be described as waves (travelling both in space and in time) The state of the particle is given by a wave function Introduction toQuantum mechanics Essential ideas 1) Uncertainty principle: Conjugates quantities of a particle (ex: position & momentum) can not be known simultaneously within a certain accuracy limit 2) Quantization: The measurement of a physical quantity in a confined system results in quanta (the measured values are discrete) 4) Extrapolation to classical mechanics: The laws of classical Newtonian mechanics are the extrapolation of the laws of quantum mechanics for large systems with very large number of particles

6. I-clicker testQuiz 1a How many terms are in the Schrodinger equation? • 1 • 2 • 3 • 4

7. Introduction toQuantum mechanics Schrödinger equation (1926) Erwin Schrödinger 1887-1961

8. the mass of the particle the Planck’s constant the potential in which the particle exists the “wave function” of the particle Introduction toQuantum mechanics Schrödinger equation But what is the physical meaning of the wave function?

9. The wave function represents the “state of the particle” Born’s Statistical interpretation probability of finding the particle at point x, at time t probability of finding the particle between points a and b at time t Introduction toQuantum mechanics Wave function

10. Introduction toQuantum mechanics Indeterminacy Quantum mechanics only offers a statistical interpretation about the possible results of a measurement • Realist Position • Orthodox position • Agnostic position

11. Introduction toQuantum mechanics Now i see… It WAS there! The realist position Where is it? I can’t see!

12. Introduction toQuantum mechanics I found it! I need to look into this cloud… The orthodox position “ observation not only disturb what is to be measured, they produce it…”

13. Introduction toQuantum mechanics NOW, I know! The agnostic position NO measure NO answer No answer until we measure it “seeing is believing”

14. I-clicker testQuiz 1b And you? What is your position? • Realist • Orthodox • Agnostic

15. The wave function evolves in a deterministic way according to the Schrödinger equation but the MEASURMENT perturbs the wave function, which then collapses to a spike centered around the measured value Introduction toQuantum mechanics The most commonly adopted position • Realist Position • Orthodox position • Agnostic position The mysterious impact of measuring…

16. A spiritual analogy… "If ye have faith ye hope for things which are not seen, but which are true" (Alma 32:21). Faith is a principle of action and power. Faith Introduction toQuantum mechanics … and the powerful act of measuring The principle of indeterminacy “seeing is knowing”

17. Example: number of siblings for each student in the class Distribution of the system Probability for a given j: Average value of j: Average value of a function of j Average value “Expectation” value Quantum mechanics Probabilities Discrete variables

18. The deviation: The standard deviation Quantum mechanics Probabilities Discrete variables Variance