Physics 451 Quantum mechanics I Fall 2012 Karine Chesnel

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

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

Introduction to Quantum mechanics Early 20 th century: Some revolutionary ideas from bright minds… Some History Werner Heisenberg Uncertainty Principle Erwin Schrödinger Schrödinger Equation Wolfgang Pauli Pauli exclusion principle

Introduction to Quantum 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) 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 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

I-clicker test Quiz 1a How many terms are in the Schrodinger equation? A.1 B.2 C.3 D.4

Introduction to Quantum mechanics Schrödinger equation (1926) Erwin Schrödinger

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

Introduction to Quantum mechanics Wave function 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 to Quantum mechanics Indeterminacy Quantum mechanics only offers a statistical interpretation about the possible results of a measurement Realist Position Orthodox position Agnostic position

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

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

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

I-clicker test Quiz 1b And you? What is your position? A.Realist B.Orthodox C.Agnostic

Introduction to Quantum mechanics Realist Position Orthodox position Agnostic position 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 The mysterious impact of measuring… The most commonly adopted position

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

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

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