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PHYSICS 360 Quantum Mechanics PHYSICS 360 Quantum Mechanics Prof. Norbert Neumeister Department of Physics and Astronomy Purdue University Spring 2020 http://www.physics.purdue.edu/phys360 Course Format • Lectures: – Time: Monday, Wednesday 9:00 – 10:15 – Lecture Room: PHYS 331 – Instructor: Prof. N. Neumeister – Office hours: Tuesday 2:00 – 3:00 PM (or by appointment) – Office: PHYS 372 – Phone: 49-45198 – Email: [email protected] (please use subject: PHYS 360) • Grader: – Name: Guangjie Li – Office: PHYS 6A – Phone: 571-315-3392 – Email: [email protected] – Office hours: Monday: 1:30 pm – 3:30 pm, Friday: 1:00 pm – 3:00 pm Purdue University, Physics 360 1 Textbook The textbook is: Introduction to Quantum Mechanics, David J. Griffiths and Darrell F. Schroeter, 3rd edition We will follow the textbook quite closely, and you are strongly encouraged to get a copy. Additional references: • R.P. Feynman, R.b. Leighton and M. Sands: The Feynman Lectures on Physics, Vol. III • B.H. brandsen and C.J. Joachain: Introduction To Quantum Mechanics • S. Gasiorowicz: Quantum Physics • R. Shankar: Principles Of Quantum Mechanics, 2nd edition • C. Cohen-Tannoudji, B. Diu and F. Laloë: Quantum Mechanics, Vol. 1 and 2 • P.A.M. Dirac: The Principles Of Quantum Mechanics • E. Merzbacher: Quantum Mechanics • A. Messiah: Quantum Mechanics, Vol. 1 and 2 • J.J. Sakurai: Modern Quantum Mechanics Purdue University, Physics 360 2 AA fewA (randomfew recommended but but but recommended) recommended) recommended) books books booksBooks B. H. Bransden and C. J. Joachain, Quantum Mechanics, (2nd B. H. H.B. H. Bransden Bransden Bransden and andand C. C. C. J. J. J. Joachain,Joachain Joachain,, QuantumQuantumQuantum Mechanics Mechanics Mechanics,,, (2nd(2 (2ndnd edition, Pearson, 2000). Classic text covers core elements of edition,edition, Pearson, Pearson, Pearson, 2000). 2000). 2000).ClassicClassic Classic text texttext covers covers core core core elements elements elements of ofadvanced of advanced quantum mechanics; strong on atomic physics. advancedquantum quantum quantum mechanics; mechanics; mechanics; strong on strongatomic strong physics. on on atomic atomic physics. physics. S.S. Gasiorowicz, Gasiorowicz, QuantumQuantumQuantum Physics Physics Physics,,, (2nd (2nd (2nd edn. edn. edn. Wiley Wiley Wiley 1996, 1996, 1996, 3rd 3rd 3rd S. Gasiorowicz, Quantum Physics, (3rd edition, Wiley, 2003). edition,edition, Wiley, Wiley, Wiley, 2003). 2003). 2003). 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Purdue University, Physics 360 3 Syllabus • Introduction to quantum mechanics • History overview of quantum theory • Review of classical mechanics • Wave function and Schrödinger equation • Postulates of quantum mechanics • Time-independent Schrödinger equation • One-dimensional time-independent problems • Mathematical formalism • Uncertainty principle • Hydrogen atom • Angular momentum • Identical particles and quantum statistics Purdue University, Physics 360 4 Mathematical Requirements • Prerequisites: PHYS 344 and PHYS 410 • Linear Algebra: 1. complex number 2. vector, vector space 3. matrix, basic matrix operations 4. linear operators • Calculus: derivative, integral • Differential equations: Linear differential equations See Appendix of your textbook if your math background needs to be refreshed and/or strengthened. Purdue University, Physics 360 5 Homework • Developing problem-solving skills – There will be 12 homework assignments (20 points each). – Final homework score will be calculated after dropping the two with the lowest score. – Problem sets will be assigned each Monday. – The homework is due and has to be brought to the lecture on Wednesday of the following week. – Students may discuss the problems with each other in a general way but should not do the homework as a group effort. No carbon copy homework sets are acceptable. Further, the problem solutions should be clearly and neatly written on one side only of standard size paper. Your fellow students should be able to read, follow and understand the solutions. The quality of the presentation counts towards the grade. Purdue University, Physics 360 6 Exams and Grades • Exams: – There will be two midterm exam and a final exam. All exams are closed-book. – Midterm Exams: Mar 2, 2020 and Apr 13, 2020 – Missing midterm: no makeups • Grades: – The final grade will be determined on the following basis: • 30% homework • 30% midterm exams (15% each) • 40% final exam – We will use plus/minus letter grades. – The exact cut-offs for letter grades will not be determined until the end of the semester. Purdue University, Physics 360 7 Quantum Theory R. Feynman I think I can safely say that nobody understands Quantum Mechanics. N. Bohr If quantum mechanics hasn't profoundly shocked you, you haven't understood it yet. A. Einstein Quantum mechanics is very impressive. But an inner voice tells me that it is not yet the real thing. The theory yields a lot, but it hardly brings us any closer to the secret of the Old One. In any case I am convinced that He doesn't play dice. Purdue University, Physics 360 8 Introduction to Quantum Mechanics A law governing the microscopic world • All objects are built of small common bricks • The behavior of large objects can be different from their elements • Classical physics describes the macroscopic world • Quantum physics describes the microscopic world • Classical physics can be considered as a natural limit of quantum mechanics by taking the Planck constant to be zero Purdue University, Physics 360 9 Quantum Mechanics • The quantum mechanical world is VERY different! – Energy not continuous, but can take on only particular discrete values. – Light has particle-like properties, so that light can bounce off objects just like balls. – Particles also have wave-like properties, so that two particles can interfere just like light does. – Physics is not deterministic, but events occur with a probability determined by quantum mechanics. Purdue University, Physics 360 10 The Quantum Mechanics View • All matter (particles) has wave-like properties – so-called particle-wave duality • Particle-waves are described in a probabilistic manner – electron doesn‘t whiz around the nucleus, it has a probability distribution describing where it might be found – allows for seemingly impossible “quantum tunneling” • Some properties come in dual packages: can’t know both simultaneously to arbitrary precision – called the Heisenberg Uncertainty Principle – not simply a matter of measurement precision – position/momentum and energy/time are example pairs • The act of “measurement” fundamentally alters the system – called entanglement: information exchange alters a particle’s state Purdue University, Physics 360 11 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 Ѱ(x,t) 4. Extrapolation to classical mechanics: The laws of classical Newtonian mechanics are the extrapolation
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