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Quantum Mechanics

Quantum mechanics is a theory in physics that was introduced by Max Planck in 1900 to solve the problem of describing the intensity of radiation emitted by a black body at a given wavelength and constant temperature. Essentially it is a modification of certain views or beliefs of the classical world, especially in relation to the motion of bodies or structureless particles. It changes in a radical way the classical view of how energy is shared in a system of particles, and it also gives properties to systems not found in classical mechanics. Classical notions of time, for example, do not hold for quantum phenomena.

Properties of Quantum Systems

One important property that has been recently discovered in quantum systems is that of entanglement, in which pairs of separate particles behave in a cooperative manner. Another very important property found only in quantum systems is particles with spin. The electron was found to have a spin value of one-half. Other particles were subsequendy discovered in nature to have other spin values, and this led eventually to the grouping of the different particles of nature according to their spin value. Particles with half-integer spin values are called fermions, with the electron as the prime example. Others with integer spin values are called bosons, with the photon (particle of light) as the most well-known example. In classical systems where the laws of Sir Isaac Newton are valid, energy is distributed according to Boltzmann statistics. However, in quantum mechanical systems, energy is distributed using Bose-Einstein or Fermi-Dirac statistics. Integer-spin particles distribute their energy in terms of Bose-Einstein statistics and half-integer-spin particles employ Fermi-Dirac statistics.

In classical mechanics, the position of a particle is measured as time changes. In mathematical terms we say position is a function of time. On the other hand, in quantum mechanics, position and time are treated as independent variables on an equal footing. Position no longer becomes a function of time. In other words, there is a given probability that a particle can be at any position at any time. It is this probability that varies with position in space and time. In classical mechanics we can predict with certainty the position of a particle at any given time. This makes quantum mechanics a statistical theory, unlike Newtonian mechanics.

Black Body Radiation

A black body is defined as one that absorbs all electromagnetic energy (radiant energy) incident on it at all wavelengths. A good approximation to a black body is a closed cavity kept at constant temperature with blackened interior walls and with a small hole that allows electromagnetic radiation to enter and exit the cavity. Measurements of the intensity (total power radiated per unit area per unit wavelength at a given temperature) of radiation emitted by a black body were independent of the physical and chemical properties of the black body but varied with the temperature T. In 1879, J. Stefan found an empirical relation between the total power emitted per unit area of a black body R (total emittance) and temperature T. Subsequently, in 1884, Ludwig Boltzmann derived the same relation from thermodynamics. This relation is known as the Stefan-Boltzmann law and is given as R = σT4 where σ = 5.7 × CT8. Wm−2K−4 is a constant known as Stefan's constant. It was also found that the intensity distribution at a given temperature had a well-defined maximum at wavelength denoted λmax. In 1893, Wilhelm Wien showed that λmax varies inversely with temperature as λmaxT = 2.898 × CT−3mK, which is called Wien's law.

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