LYCOS RETRIEVER
Quantum Mechanics
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An important aspect of Quantum Mechanics is the predictions it makes about the radioactive decay of isotopes. Radioactive decay processes, controlled by the wave equations, are random events. A radioactive atom has a certain probability of decaying per unit time. As a result, the decay results in an exponential decrease in the amount of isotope remaining in a given sample as a function of time. The characteristic time required for 1/2 of the original amount of isotope to decay is known as the "half-life" and can vary from quadrillionths of a second (9B) to quintillions of years (186W).
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Perhaps some mention of the problem that inspired Planck to invent Quantum Mechanics is in order. IIRC, physicists were trying to figure out what electromagnetic waves were in an oven that had a certain amount of heat in it. They knew that an integer multiple of the wavelength of the light in the oven would have to equal one of the dimensions of the oven, but every time they tried to figure it out, they ended up concluding that the oven had infinite energy in it. Planck was able to find the answer by assume that the energy in an electromagnetic wave was quantised such that E ∝ f. This went directly counter to the classical mechanics assumtion that E ∝ Amplitude.
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This has now been shown to actually occur on the basis of Bell's Theorem (from John Bell, 1928-1990), meaning that Quantum Mechanics does violate Special Relativity by allowing instantaneous interactions across even cosmological distances. However, once observed, processes must still obey Special Relativity and the limitations of spatial distance, creating the kind of duality described by Kant. Bell himself found this result disturbing, but to Kant it would fit in with his own theory that space is only imposed by the representation of phenomenal objects.
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By emphasizing the application of quantum science to devices which students see frequently, the Visual Quantum Mechanics materials help students understand that quantum science is all around them. Without quantum science they could not have television remotes, fluorescent lamps or many other everyday devices.
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The course is intended as an introduction to the methods of Quantum Mechanics. It will be assumed that the student has already some familiarity with ordinary and partial differential equations, linear algebra and Fourier transforms. Third-year courses in Electromagnetism and Classical Mechanics are prerequisites. Topics to be covered during the fall quarter will include:
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When quantum mechanics was originally formulated, it was applied to models whose correspondence limit was non-relativistic classical mechanics. For instance, the well-known model of the quantum harmonic oscillator uses an explicitly non-relativistic expression for the kinetic energy of the oscillator, and is ... a quantum version of the classical harmonic oscillator.
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