Quantum mechanics

Video: Lecture 1 | Modern Physics: Quantum Mechanics (Stanford)

Lecture 1 of Leonard Susskind’s Modern Physics course concentrating on Quantum Mechanics.  Recorded January 14, 2008 at Stanford University.

Category : Education

LICENSE: Creative Commons (Attribution-Noncommercial-No Derivative Works).

 

Quantum mechanics

Quantum mechanics (QM – also known as quantum physics, or quantum theory) is a branch of physics which deals with physical phenomena at microscopic scales, where the action is on the order of the Planck constant.

The name quantum mechanics derives from the observation that some physical quantities can change only in discrete amounts (Latin quanta), and not in a continuous (cf. analog) way. For example, the angular momentum of an electron bound to an atom or molecule is quantized. In the context of quantum mechanics, the wave–particle duality of energy and matter and the uncertainty principle provide a unified view of the behavior of photons, electrons, and other atomic-scale objects.

The history of quantum mechanics

The earliest versions of quantum mechanics were formulated in the first decade of the 20th century.

At around the same time, the atomic theory and the corpuscular theory of light (as updated by Einstein) first came to be widely accepted as scientific fact; these latter theories can be viewed as quantum theories of matter and electromagnetic radiation, respectively.

Early quantum theory was significantly reformulated in the mid-1920s by Werner Heisenberg, Max Born and Pascual Jordan, who created matrix mechanics; Louis de Broglie and Erwin Schrödinger (Wave Mechanics); and Wolfgang Pauli and Satyendra Nath Bose (statistics of subatomic particles). Moreover, the Copenhagen interpretation of Niels Bohr became widely accepted.

By 1930, quantum mechanics had been further unified and formalized by the work of David Hilbert, Paul Dirac and John von Neumann, with a greater emphasis placed on measurement in quantum mechanics, the statistical nature of our knowledge of reality, and philosophical speculation about the role of the observer.

Quantum mechanics has since branched out into almost every aspect of 20th century physics and other disciplines, such as quantum chemistry, quantum electronics, quantum optics, and quantum information science.

Much 19th century physics has been re-evaluated as the “classical limit” of quantum mechanics, and its more advanced developments in terms of quantum field theory, string theory, and speculative quantum gravity theories.

The history of quantum mechanics is a fundamental part of the history of modern physics.

Quantum mechanics’ history, as it interlaces with the history of quantum chemistry, began essentially with a number of different scientific discoveries:

  • the 1838 discovery of cathode rays by Michael Faraday;
  • the 1859-1860 winter statement of the black body radiation problem by Gustav Kirchhoff;
  • the 1877 suggestion by Ludwig Boltzmann that the energy states of a physical system could be discrete;
  • the discovery of the photoelectric effect by Heinrich Hertz in 1887;
  • and the 1900 quantum hypothesis by Max Planck that any energy-radiating atomic system can theoretically be divided into a number of discrete “energy elements” ε (epsilon) such that each of these energy elements is proportional to the frequency ν with which each of them individually radiate energy, as defined by the following formula:

ε = hν,   where h is a numerical value called Planck’s constant.

  • Then, Albert Einstein in 1905, in order to explain the photoelectric effect previously reported by Heinrich Hertz in 1887, postulated consistently with Max Planck’s quantum hypothesis that light itself is made of individual quantum particles, which in 1926 came to be called photons by Gilbert N. Lewis. The photoelectric effect was observed upon shining light of particular wavelengths on certain materials, such as metals, which caused electrons to be ejected from those materials only if the light quantum energy was greater than the Fermi level (work function) in the metal.

The phrase “quantum mechanics” was coined (in German, “quantenmechanik”) by the group of physicists including Max Born, Werner Heisenberg, and Wolfgang Pauli, at the University of Göttingen in the early 1920s, and was first used in Born’s 1924 paper “Zur Quantenmechanik”. In the years to follow, this theoretical basis slowly began to be applied to chemical structure, reactivity, and bonding.

A quantum dot is Nanotechnology?

Nanotechnology (sometimes shortened to “nanotech”) is the manipulation of matter on an atomic and molecular scale.

A quantum dot is a particle of matter so small that the addition or removal of an electron changes its properties in some useful way. All atoms are, of course, quantum dots, but multi-molecular combinations can have this characteristic.

In biochemistry, quantum dots are called redox groups.

In nanotechnology , they are called quantum bits or qubit s.

Quantum dots typically have dimensions measured in nanometers, where one nanometer is 10 -9 meter or a millionth of a millimeter.

Applications of a quantum dot

Quantum dots are particularly significant for optical applications due to their high extinction coefficient. In electronic applications they have been proven to operate like a single electron transistor and show the Coulomb blockade effect. Quantum dots have also been suggested as implementations of qubits for quantum information processing.   The ability to tune the size of quantum dots is advantageous for many applications.

For instance, larger quantum dots have a greater spectrum-shift towards red compared to smaller dots, and exhibit less pronounced quantum properties. Conversely, the smaller particles allow one to take advantage of more subtle quantum effects.   Researchers at Los Alamos National Laboratory have developed a wireless device that efficiently produces visible light, through energy transfer from thin layers of quantum wells to crystals above the layers.

Being zero dimensional, quantum dots have a sharper density of states than higher-dimensional structures.

As a result, they have superior transport and optical properties, and are being researched for use in diode lasers, amplifiers, and biological sensors.

Quantum dots may be excited within a locally enhanced electromagnetic field produced by gold nanoparticles, which can then be observed from the surface plasmon resonance in the photoluminescent excitation spectrum of (CdSe)ZnS nanocrystals.

High-quality quantum dots are well suited for optical encoding and multiplexing applications due to their broad excitation profiles and narrow/symmetric emission spectra.

The new generations of quantum dots have far-reaching potential for the study of intracellular processes at the single-molecule level, high-resolution cellular imaging, long-term in vivo observation of cell trafficking, tumor targeting, and diagnostics.

Computing

Quantum dot technology is one of the most promising candidates for use in solid-state quantum computation. By applying small voltages to the leads, the flow of electrons through the quantum dot can be controlled and thereby precise measurements of the spin and other properties therein can be made. With several entangled quantum dots, or qubits, plus a way of performing operations, quantum calculations and the computers that would perform them might be possible.

Biology

In modern biological analysis, various kinds of organic dyes are used. However, with each passing year, more flexibility is being required of these dyes, and the traditional dyes are often unable to meet the expectations. To this end, quantum dots have quickly filled in the role, being found to be superior to traditional organic dyes on several counts, one of the most immediately obvious being brightness (owing to the high extinction co-efficient combined with a comparable quantum yield to fluorescent dyes) as well as their stability (allowing much less photobleaching). It has been estimated that quantum dots are 20 times brighter and 100 times more stable than traditional fluorescent reporters.

The usage of quantum dots for highly sensitive cellular imaging has seen major advances over the past decade. The improved photostability of quantum dots, for example, allows the acquisition of many consecutive focal-plane images that can be reconstructed into a high-resolution three-dimensional image. Another application that takes advantage of the extraordinary photostability of quantum dot probes is the real-time tracking of molecules and cells over extended periods of time. Antibodies, streptavidin, peptides, nucleic acid aptamers, or small-molecule ligands can be used to target quantum dots to specific proteins on cells.

Photovoltaic devices

Quantum dots may be able to increase the efficiency
and reduce the cost of today’s typical silicon photovoltaic cells. According to
an experimental proof from 2004, quantum dots of lead selenide can produce more
than one exciton from one high energy photon via the process of carrier
multiplication or multiple exciton generation (MEG). This compares favorably to
today’s photovoltaic cells which can only manage one exciton per high-energy
photon, with high kinetic energy carriers losing their energy as heat. Quantum
dot photovoltaics would theoretically be cheaper to manufacture, as they can be
made “using simple chemical reactions.”

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