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Lecture 27

# Lecture 27 - Lecture 27 Quantum Physics Atoms Final Exam...

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Lecture 27 Atoms

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Final Exam 3 Long Answer [20+20+20 = 60] 3 Short Answer [10+10+10 = 30] 10 MT [3 x 10 = 30] Wed 10:30am-12:30pm Bring ID + approved calculator Same Seating Chart as Midterm 1/3 pre-midterm material [similar to problems you have seen on midterm or quizzes] 2/3 new material [material covered in homework]
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 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
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. - | ψ (x)| 2 dx = 1

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A Particle in a Box o Classically, the particle could have any energy E or speed v, and it could be located anywhere inside the box o In quantum mechanics, it’s different…
Boundary Conditions o The particle cannot pass through the walls, so its wave function must be zero at x=0 and x=L Similar, in this case, to a standing wave o ψ (0) = 0 o ψ (L) = 0

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Wavefunction for particle in box o Wavefunction is an ideal sin wave: ψ (x) = A sin kx = A sin(2 π x/ λ ) (for 0 < x < L) λ = 2L/n from boundary conditions, so ψ (L) = sin(2 π L/ λ ) = 0 Therefore ψ (x) = A sin(n π x/L) (n = 1, 2, 3,…) [nothing in between] Wavefunction ψ Probability Density ψ 2 n = 3 n = 2 n = 1
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Lecture 27 - Lecture 27 Quantum Physics Atoms Final Exam...

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