Course Format • Lectures: – Time: Tuesday, Thursday 10:30 – 11:45 – Lecture Room: PHYS 331 – Instructor: Prof. N. Neumeister – Office hours: Tuesday 2:00 – 3:00 PM (or by appointment) – Office: PHYS 374 – Phone: 49-45198 – Email: [email protected] (please use subject: PHYS 460) • Grader: – Jun Cheng – Office: PHYS 285 – Phone: 765 464-9735 – Email: [email protected] – Office hours: Wednesday: 11:00-12:00 am, Thursday: 9:00-10:00 am, 3:00-4:00 pm Purdue University, Physics 460 1 Textbook The textbook is: Introduction to Quantum Mechanics, David J. Griffiths, 2nd 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 460 2 Syllabus • Introduction to quantum mechanics • History overview of quantum theory • Wave function and Schrödinger Equation • Postulates of Quantum Mechanics • Time-independent Schrödinger Equation • One-dimensional time-independent problems • Mathematical formalism • Heisenberg quantum mechanics and uncertainty principle • Hydrogen atom • Angular momentum • Identical particles and quantum statistics Purdue University, Physics 460 3 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 460 4 Homework • Developing problem-solving skills – There will be approximately 12 homework assignments. – Problem sets will be assigned each Tuesday. – The homework is due and has to be brought to the lecture on Thursday 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 460 5 Exams and Grades • Exams: – There will be one midterm exam and a final exam. All exams are closed-book. – Midterm Exam: October 20, 2011 • Grades: – The final grade will be determined on the following basis: • 30% homework • 30% midterm exam • 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 460 6 Quantum Mechanics • 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. • N. Bohr If quantum mechanics hasn't profoundly shocked you, you haven't understood it yet. • R. Feynman I think I can safely say that nobody understands Quantum Mechanics. Purdue University, Physics 460 7 Introduction to Quantum Mechanics A law governing 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 460 8 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 460 9 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 460 10 History of Quantum Mechanics Purdue University, Physics 460 11 Classical Physics • Before 1900: Classical physics claimed a full victory Classical Electrodynamics Classical Statistical Newton’s Law and Gravity Physics Purdue University, Physics 460 12 Atomic Hypothesis • Around 1900: The atomic hypothesis became popular • 1897: J.J. Thomson – discovery of the electron • 1905: E. Rutherford – atomic model • 1910: Millikan measures the electric charge – it’s quantized • If the model is right, it is the end of classical mechanics. • How can an atom be stable? • Energy would be lost by radiation. • Surrounding Electrons would have collapsed to nuclear. There must be new physical laws! Purdue University, Physics 460 13 Atomic Hypothesis • Around 1900: The color of atoms • Different atoms glowed in different colors • Optical spectrum of atoms: characteristic of the elements • Balmer (1885) found an ordering principle in atomic spectra Optical spectra of Calcium Purdue University, Physics 460 14 The Black Body Spectrum • Light radiated by an object characteristic of its temperature, not its surface color. • Spectrum of radiation changes with temperature Purdue University, Physics 460 15 The Black Body Spectrum • The wavelength of the peak of the blackbody distribution was found to follow constant !max = Temperature • Peak wavelength shifts with temperature • λ max is the wavelength at the curve’s peak • T is the absolute temperature of the object emitting the radiation Purdue University, Physics 460 16 Classical Theory • Classical physics had absolutely no explanation for this. • Only explanation they had gave ridiculous answer. • Amount of light emitted became infinite at short wavelength – Ultraviolet catastrophe Purdue University, Physics 460 17 Explanation by Q.M. • Blackbody radiation spectrum could only be explained by quantum mechanics. • Radiation made up of individual photons, each with energy (Planck’s const) x (frequency). • Very short wavelengths have very high energy photons. • Minimum energy is 1 photon. • For shorter wavelengths even 1 photon is too much energy, so shortest wavelengths have very little intensity. Purdue University, Physics 460 18 Heat Radiation Planck • Black body radiation: Each mode carries discrete energy quanta: E=hν Planck: I can characterize the whole procedure as an act of desperation, since, by nature I am peaceable and opposed to doubtful adventures. However, I had already fought for six years (since 1894) with the problem of equilibrium between radiation and matter without arriving at any successful result. I was aware that this problem was of fundamental importance in physics, and I knew the formula describing the energy distribution . hence a theoretical interpretation had to be found at any price, however high it might be. Purdue University, Physics 460 19 Einstein: Light energy is quantized Photoelectric effects: (1905) Specific heat in solids (1907) • Current is only generated with the frequency of • Specific heat is a constant in classical statistical physics the light higher than a threshold. • Einstein-Debye model: lattice vibration energy is quantized • Specific heat is temperature dependent. • No matter how large is the power of light, there is no electric current if the frequency of the light is below the threshold. Purdue University, Physics 460 20 Bohr atom (1913) • Electron orbits in an atom are quantized • Each orbits have their own energy • The absorbed light is exactly such that the photon carries the energy difference between the two orbits Bohr-Sommerfeld quantization: Purdue University, Physics 460 21 The Birth of Quantum Mechanics • Bohr’s theory failed: At the turn of the year from 1922 to 1923, the physicists looked forward with enormous enthusiasm towards detailed solutions of the outstanding problems, such as the helium problem and the problem of the anomalous Zeeman effects. However, within less than a year, the investigation of these problems revealed an almost complete failure of Bohr's atomic theory. (Quote from Jagdish Mehra and Helmut Rechenberg: monumental history of quantum mechanics) • Rapid development in 1920’s (modern quantum mechanics) • De Broglie wave=particle (1923, age 31) • Heisenberg Matrix theory (1925, age 23) • Erwin Schrodinger wave equations