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Unformatted text preview: Lecture 26 Quantum Physics V "I think it is safe to say that no one understands quantum mechanics. Do not keep saying to yourself' But how can it be like that ?' because you will go into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that ."Richard Feynman Review o Light travels like a wave It Refracts Shows Interference Exhibits the Doppler effect o Light hits like a particle! Photoelectric effect Compton Scattering This particlewave duality is intimately linked to the theory of Quantum Mechanics Matter Particle and Wave? o de Broglies idea: For a general particle, we can also talk about a wave with some amplitude. The square of this amplitude is the probability probability that a particle exists at that location. Psi is called the Wave Function. Probability Probability Density o The squared wavefunction represents a probability density of a particle being at one location. o Vertical direction is probability, horizontal is location along a line. (imagine a particle on a string) o The most likely position of the particle associated with this wavefunction is at the peak of the curve. Probability Density o Mathematically the probability density is: P(x) dx =  (x) 2 dx o Probability that particle is located within a small region around x. o Integrate it to get the probability for the particle to be in a specific region between a and b: a b  (x) 2 dx = probability particle is between a and b Area beneath curve is a probability The Wave Function o According to QM, all available information about a system is represented by a wave function, (x) For a particle with definite momentum: (x) = sin(kx) o The QM wave function describes the wavelike behavior of matter and is analogous to the oscillating E and B vectors in EM waves o The QM wavefunction represents a probability amplitude o Square the wavefunction to get the probability of finding the particle near a certain location Always positive Normalization of the Wavefunction o Since the particle must be somewhere , we require that the integral of the probability density over all possible coordinate values is equal to 1....
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This note was uploaded on 09/08/2008 for the course PHYS 3B taught by Professor Wu during the Spring '08 term at UC Irvine.
 Spring '08
 Wu
 mechanics, Quantum Physics

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