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.
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.
Quantum Mechanics Theory And Experiment Mark Beck.pdfl
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.
In 1994 Beck took a visiting faculty position at Reed College because of his attraction to teaching and working with undergraduates on research. During his time at Reed he began working with students on modern quantum optics experiments. In 1996 Beck moved to Whitman College, and shortly after that he, and others, realized that advances in laser technologies, nonlinear optics and electronics were on the verge of making it possible and affordable to construct apparatus to perform fundamental experimental tests of quantum theory in an undergraduate teaching laboratory.
Beck and several of his undergraduate students designed and produced such apparatus and, with it, tested quantum mechanical predictions in teaching laboratories. In addition to demonstrating the single-photon nature of light emitted in certain nonlinear-optical experiments, his students were able to verify that local realism is violated in Hardy's test, providing strong support for the quantum nature of the physical world. These tests also served to demonstrate quantum entanglement, a uniquely quantum feature, which underlies efforts to build quantum computers. The fact that undergrads could see for themselves the quantum nature of light, and learn modern optical techniques at the core of quantum information science, was revolutionary.
Because each of the BBO crystals emits light of the same energy in cones that overlap, a detector placed in the appropriate position has a nearly equal chance of seeing horizontally and vertically polarized downconverted photons. Moreover, until some sort of measurement of polarization is applied to the system, the two types of photons are indistinguishable. Because of this, according to the rules of quantum mechanics, these photons are in a superposition of the two possibilities- the possibility of a pair of horizontally polarized photons or a pair of vertical ones. This makes the photons entangled. To understand this, it is helpful to think of the double-slit experiment. In that setup, we said that particles arriving at the screen could have come through the left or right slit, so in fact until measured they exist in a superposition of the two. There are two differences to keep in mind, however. The first is that in the double slit experiment, these two possibilities interfere constructively and destructively at different points on the screen, producing fringes, but in our entanglement setup we keep the phase relationship between the paths constant. This is rather like if you imagine shrinking the double-slit screen until it only covers the central bright fringe. The second is that our two possibilities now correspond to two particles, not one, which is why this system is entangled.
We will be measuring a quantity called S. S cannot be greater than 2 for a system that obeys local realism, but according to quantum mechanics can be as high as $2\sqrt2$. Thus, any result that is greater than 2 and not due to chance (ie at least a standard deviation or two away) can be considered a violation of Bell's Inequality.
Enrique Galvez in the Physics and Astronomy Department at Colgate developed 5 lab exercises in quantum mechanics with funding from two NSF CCLI grants for advanced lab courses. His web site has links to lab writeups for each experiment, and a "lab manual" (first link under "Free Downloads") that provides detailed instructions on building the experiments. This document lists a variety of options for lasers, other optical components, and detectors with discussion of their pros and cons.
It is widely accepted that consciousness or, more generally, mentalactivity is in some way correlated to the behavior of the materialbrain. Since quantum theory is the most fundamental theory of matterthat is currently available, it is a legitimate question to askwhether quantum theory can help us to understand consciousness.Several approaches answering this question affirmatively, proposed inrecent decades, will be surveyed. There are three basic types ofcorresponding approaches: (1) consciousness is a manifestation ofquantum processes in the brain, (2) quantum concepts are used tounderstand consciousness without referring to brain activity, and (3)matter and consciousness are regarded as dual aspects of oneunderlying reality. Major contemporary variants of thesequantum-inspired approaches will be discussed. It will be pointed outthat they make different epistemological assumptions and use quantumtheory in different ways. For each of the approaches discussed, bothproblematic and promising features will be highlighted.
Quantum theory introduced an element of randomness standing outagainst the previous deterministic worldview preceding it, in whichrandomness expresses our ignorance of a more detailed description (asin statistical mechanics). In sharp contrast to such epistemicrandomness, quantum randomness in processes such as the spontaneousemission of light, radioactive decay, or other examples has beenconsidered a fundamental feature of nature, independent of ourignorance or knowledge. To be precise, this feature refers toindividual quantum events, whereas the behavior ofensembles of such events is statisticallydetermined. The indeterminism of individual quantum events isconstrained by statistical laws.
Other features of quantum theory, which became attractive indiscussing issues of consciousness, were the concepts ofcomplementarity and entanglement. Pioneers of quantum physics such asPlanck, Bohr, Schrödinger, Pauli (and others) emphasized thevarious possible roles of quantum theory in reconsidering the oldconflict between physical determinism and conscious free will. Forinformative overviews with different focal points see e.g., Squires(1990), Kane (1996), Butterfield (1998), Suarez and Adams (2013). 2ff7e9595c
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