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Lecture 26 (29.2-29.3)

# Lecture 26 (29.2-29.3) - Lecture 26 Quantum Physics V"I...

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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

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Review o Light travels like a wave It Refracts Shows Interference Exhibits the Doppler effect o Light “hits” like a particle! Photo-electric effect Compton Scattering This particle-wave “duality” is intimately linked to the theory of Quantum Mechanics Matter – Particle and Wave? o de Broglie’s 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

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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 = | ψ (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 | ψ (x)| 2 dx = probability particle is between a and b Area beneath curve is a probability

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The Wave Function o According to QM, all available information about a system is represented by a wave function, Ψ (x) For a particle with definite momentum: Ψ (x) = sin(kx) o The QM wave function Ψ 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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Lecture 26 (29.2-29.3) - Lecture 26 Quantum Physics V"I...

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