Quantum Mechanics Theory And Experiment Mark Beck.pdf
Handouts: some notes/comments A listing of the basic rules (`postulates') of quantum mechanics. The formal definition of hermitian conjugates. Averaging continuous vs discrete variables. A discussion of one way to think of wavefunctions as vectors. Probability densities versus probability amplitudes versus just probabilities. Measurement of a spin-1/2 object. Scanned lecture notes Scanned lecture notes, part A.
Quantum Mechanics Theory And Experiment Mark Beck.pdf
Textbooks and other Sources Quantum mechanics is counter-intuitive. There will be confusing aspects; you will need to invest time and effort to clear up these confusions.Do not expect to get comfortable with QM unless you do a fair amount of reading and problem-solving. It is strongly recommended that you work through one or more texts. Working through Prof. Nash's lecture notes is an absolute minimum. It would be a very good idea to read a couple of sections every week.Additional texts are listed below, and there are links to lecturenotes etc. There are many textbooks on introductory quantum mechanics(e.g., carried by the Maynooth library, physically and as e-books).Textbooks have differences in ordering and notation, but you shouldbenefit by reading any text.Please let me know if any of the links below are broken. Overviews of Introductory Quantum Mechanics: MP363 lecture notes of Prof. Charles Nash Please aim to understand ALL of the material in these notes. Theclass will not follow the ordering but you are expected to pick up allconcepts at the level of these notes.
Dirac notation (bra-ket notation) and properties of bra's and ket's: Please get comfortable with this mathematical formulation. Chapter2 of Nash notes introduces most of the notation. Here are some more references:Wikipedia pages: page on Bra-Ket notation and page on orthonormal basis. Notes P. Kok. The first chapter summarizes bra-ket notation,operators, etc. Try digesting the first three sections.(The rest of the notes are rather advanced.) Overview of the Mathematical Formalism of QM, from notes of Bertlmann. From the notes of J.Cresser: for the mathematical formalism, try Chapter 8,Chapter 9, and Chapter 10,On bra-ket notation: A chapter titled `Dirac's Bra and Ket Notation', from some lecture notes. Spin-1/2 systems: This topic is not covered in Nash's notes. We will use the spin-1/2 system for many examples; so it is important that you get familiar through other sources. Some links below.Link 1: Notes on Spin-1/2 systems. Please read Sections 2 and 3 at least.Link 2: A Chapter on Spin-1/2 systems and Pauli matrices. Postulates of Quantum Mechanics:Not covered in Nash's notes. The numbering of postulates varies (isnot standardized), but each treatment covers very similar statements. Link 1: Notes by Jaffe, MIT. The postulates are discussed in section 1 of these notes. Link 2: Wikipedia. The Dirac delta function: Notes on the delta function from various people:a link, another link, another link, another link, another link. another link. Wikipedia page on the delta function. If the potential experienced by a particle has the form of a dirac delta function, you can solve for the bound states as well as the scattering states: Wikipedia page on the Dirac delta potential in quantum mechanics.Another link covering the topic.You are expected to be able to calculate properties of the boundstate and also calculate transmission and reflection coefficients forscattering states.Sources for other topics: Two slit inteference: Here is a careful description of two-slit interference. Please readthrough: this topic is not covered in Nash's notes. Wikipedia article on `Wave-particle duality'. Includes discussion and animation of interference. Review of the Birth of Quantum Mechanics (from lecture notes by M.Fowler). This nicely supplements Chapter 1 of Nash's notes.From notes of J.Cresser: Early History of Quantum Mechanics Useful wikipedia pages: momentum operator;position operator;Schroedinger equation;Self-adjoint (hermitian) operator;Unitary operator;Uncertainty principle.Textbooks: There are many textbooks available on introductory quantum mechanics. I list some sources below.(I omit publisher and year of publication: the author and titleshould be enough to identify each textbook.)Volume III of The Feynman Lectures on Physics ; can be read online. D. J. Griffiths, Introduction to Quantum Mechanics. D. A. Miller, Quantum Mechanics for Scientists and Engineers. M. Beck, Quantum Mechanics: Theory and Experiment. J. S. Townsend, A Modern Approach to Quantum Mechanics.
I'm really interested in quantum theory and would like to learn all that I can about it. I've followed a few tutorials and read a few books but none satisfied me completely. I'm looking for introductions for beginners which do not depend heavily on linear algebra or calculus, or which provide a soft introduction for the requisite mathematics as they go along.
is heavy on good exercizes and mathematical tools. L&L include topics not covered everywhere else. The standard undergraduate books on quantum mechanics are not very good in comparison to these, and should not be used.
You can also read the Wikipedia page on old quantum theory for a sketchy summary, then look at the page on matrix mechanics. This explains the intuition Heisenberg had about matrix elements, something which is not in Dirac's book or anywhere else. Heisenberg's reasoning is also found to certain extent in the first chapters of this book:
Next, watch the "Theorectical Minimum" videos by Leonard Susskind . They represent the theoretical minimum that you need to know about quantum mechanics. (i.e. the title of the video course is theoretical minimum, but it is in fact a course on quantum mechanics. Susskind is a great teacher and the videos are great. You can access them on itunes and You Tube. Search for Susskind lectures quantum mechanic from Stanford. They are just released (a few weeks ago)
If you are not willing to learn the linear algebra upon which the entire theory of quantum mechanics is based, then you really aren't going to have much luck finding the kind of textbook you seek. It sounds to me like what you want is a textbook that introduces you to what is called "modern physics" instead. Most "modern physics" texts cover quantum mechanics concepts while remaining mostly in algebra land. Most of the textbooks recommended in the answers posted before mine are chock full of calculus.
I used this book the last time I taught quantum mechanics, and the students really liked it a lot. You can teach yourself "real" quantum mechanics from this book using the Dirac bra-ket notation used in real physics research and in quantum information theory.
Here you will find the same story as physicists tell there own students. The difference is that this book is designed to be much easier to read and understand than comparable texts. Quantum mechanics is inherently mathematical, and this book explains it fully. But the mathematics is only covered to the extent that it provides insight in quantum mechanics. This is not a book for developing your skills in clever mathematical manipulations that have absolutely nothing to do with physical understanding. You can find many other texts like that already, if that is your goal.
No calculus is found in this book. All concepts in linear algebra are introduced. Unfortunately, this means you won't encounter stuff like the Schrodinger equation. You will have a much better than PBS understanding of quantum mechanics (what is quantum state, how you can add states, probability in quantum mech, etc.). Lightweight and cheap!
Feynman's Six Easy Pieces is an excellent introduction to quantum mechanics. For a more thorough analysis (and some philosophical ruminations), I'd recommend The Dancing Wu Li Masters by Gary Zukav. For an easy-to-understand discussion of the weirdness of quantum mechanics, Fred Kuttner and Bruce Rosenblum's Quantum Enigma: Physics Encounters Consciousness is excellent.
A quantum mechanics primer by Gillespie is good. Is only 125 pages long. It starts covering the basic mathematical tools from the ground: probability, complex numbers, vectors, operators in Hilbert space, and a review of classical mechanics including the Hamilton formulation. Then goes through the quantum mechanics postulates with simple, yet accurate math. It uses a notation slightly different from the Dirac bra-ket notation but it is in essence the same, perhaps more readable for newbies.The main strong point is that it does not suppose any previous knowledge but basic calculus, and yet it gives a reasonable understanding of the basic formalism and its meaning.
Quantum mechanics is a rather rich-in-concept subject which you cannot learn from a single book. So in this answer I am providing a list of the books on the subject that I found to be useful in understanding the quantum world.
There is an excellent book called "The Road to Reality" by Roger Penrose. It is an interesting mix, being written in a conversational, easy going and accessible way, with brilliant and insightful descriptions from a real master of the craft. However, it does not skimp on the mathematics. If you are serious about exploring quantum mechanics, and fundamental physics more generally, this great place to look. It is a fun, though not so easy, ride.
Theory of angular momentum: Rotations: Finite/infinite rotations, Commutation; Spin-1/2 system; Pauli 2-component quantum mechanics; Continuous groups: SO(3), SU(3), Euler rotations; Density operators: Pure-vs-mixed ensembles, time-evolution of ensembles, Quantum statistical mechanics; Eigenvalues and eigenstates of angular momentum; Orbital angular momentum: Spherical harmonics; Central potential problems, Hydrogen atom; Angular momentum algebra: Angular momentumaddition,Clebsh-Gordon coefficients; Oscillator model of angular momentum; Spin correlation measurements; Tensor operators: Wigner-Eckart theorem