Transcript Physics 451
Physics 451 Quantum mechanics I Fall 2012 Karine Chesnel 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 Introduction to Quantum mechanics Some History Until 20th century: Classical Newtonian Mechanics… Newton’s second Law ma F Kinetic energy 1 T mv 2 2 Mechanical energy of the system dp F dt E T V Deterministic view: All the parameters of one particle can be determined exactly at any given time Introduction to Quantum mechanics Some History Early 20th century: Some revolutionary ideas from bright minds… Werner Heisenberg 1901-1976 Erwin Schrödinger 1887-1961 Wolfgang Pauli 1900- 1958 Uncertainty Principle Schrödinger Equation 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 ( x, t ) 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) 2 2 i V 2 t 2m x Erwin Schrödinger 1887-1961 Introduction to Quantum mechanics Schrödinger equation 2 2 i V 2 t 2m x m the mass of the particle the Planck’s constant h 1.05 1034 Js 2 V the potential in which the particle exists the “wave function” of the particle But what is the physical meaning of the wave function? Introduction to Quantum mechanics Wave function The wave function ( x, t ) represents the “state of the particle” Born’s Statistical interpretation ( x, t ) 2 probability of finding the particle at point x, at time t b ( x, t ) a 2 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 I need to look into this cloud… The orthodox position 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 No answer until we measure it NOW, I know! “seeing is believing” I-clicker test Quiz 1b And you? What is your position? A. Realist B. Orthodox C. Agnostic Introduction to Quantum mechanics The most commonly adopted position • 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… Introduction to Quantum mechanics The principle of indeterminacy … and the powerful act of measuring “seeing is knowing” A spiritual analogy… Faith "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. Quantum mechanics Probabilities Discrete variables Distribution of the system Probability for a given j: N ( j) N ( j) P( j ) N Average value of j: j jP( j ) j 0 Average value of a function of j Average value f ( j ) f ( j ) P( j ) j 0 “Expectation” value Example: number of siblings for each student in the class Quantum mechanics Probabilities Discrete variables j j j The deviation: j 0 Variance j j j 2 The standard deviation 2 2 j 2 j 2 2