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Download Quantum Mechanics Lecture 1 Dr. Mauro Ferreira
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Quantum Mechanics Lecture 1 Dr. Mauro Ferreira E-mail: [email protected] Room 2.49, Lloyd Institute Course prerequisites: It is assumed that you have a working knowledge of fundamental mathematical methods. lly • Calculus; • Complex variables; • Linear algebra • Differential equations a c i t a m e h t a e s M r : g u n o i c n r e a s n W inte • Additional tools will be introduced Furthermore ... • Classical mechanics; • Electromagnetism; • Introductory Modern Physics; Objectives: By the end of this lecture you should be able to: • Recognize the need for a new theory that deals with matter in reduced scales; • Enunciate the postulates of Quantum Mechanics History By the end of the 19th century... Matter and radiation were described by Newtonian Mechanics and Maxwell’s equations, respectively Interaction between matter and radiation was explained by the Lorentz force Particle and wave properties were mutually exclusive History Blackbody radiation Photoelectric effect r a l Compton effect u c s u p r o c n o a i t d a i e d c a u r d f o o r t In spect a Louis de Broglie proposed that not only waves behave like particles but that all matter should also have a wave-like behaviour h λ= p wavelength 3 2 19 E ν= h frequency History Wave aspects of particles Matter waves and the de Broglie hypothesis Davisson-Germer experiment • Consider the following experiment: “classical” particles are allowed through a narrow gap. The blue curve displays how they are spatially distributed ... and now through two separate gaps. The distribution is just a simple addition of the two individual distributions • The double slit experiment with electrons displays interference patterns • Now suppose that we try to determine which slit the electron has moved through. In this case, the interference pattern disappears. • The double slit experiment with electrons displays interference patterns • Now suppose that we try to determine which slit the electron has moved through. In this case, the interference pattern disappears. Complementarity Principle: Particle and wave properties are not mutually exclusive, but complementary An experiment designed to isolate the particle features of a quantum system gives no information about its wave features and vice-versa. In summary: Corpuscular aspects of radiation and wave aspects of particles Blackbody radiation Photoelectric effect Compton effect Matter waves and the de Broglie hypothesis Davisson-Germer experiment Wave-particle duality and complementarity principle • Emission spectrum of the Hydrogen atom not explained by classical Physics • Explained by Bohr’s atomic model, who introduced the concept of stationary orbits of quantized angular momentum 3 1 19