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Midterm Review - Physics 214 Midterm Review Notes Anne C...

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Physics 214 Midterm Review Notes Anne C. Hanna [email protected] June 6, 2005 Contents 1 Disclaimers and usage notes 3 2 Everyday waves: the wave equation 3 2.1 Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 General properties of sinusoidal solutions . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Properties specific to wave equation sinusoids . . . . . . . . . . . . . . . . . . . . . . 6 3 Interference 6 3.1 Two sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.1.1 Identical nearby sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.1.2 Identical distant sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.1.3 Non-identical sources (phasors and the law of cosines) . . . . . . . . . . . . . 8 3.2 More than two sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.2.1 Non-identical sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.2.2 Identical sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 4 Diffraction 13 4.1 Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 4.2 Circular Apertures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1
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4.3 Diffraction limitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 4.4 Phasors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 5 Mixed interference and diffraction 15 6 Particles as waves 16 6.1 The photoelectric effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 6.2 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 6.2.1 Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 6.2.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 6.2.3 The Duane-Hunt law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 6.2.4 A note on electron-Volts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 6.3 The two-slit experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 6.4 Wave-particle formulas and factoids . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 6.5 Photons and the wave equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 6.6 Massive particles and the Schroedinger equation . . . . . . . . . . . . . . . . . . . . 23 7 Wavefunctions and probability densities for massive particles 23 2
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1 Disclaimers and usage notes These midterm notes are not necessarily complete, correct, or even useful. And even if they were, they shouldn’t be your only review materials. Look through the text and the lecture notes, and try some practice exams too, please! Anything you’ve had to apply in this course, whether it be in homework, discussion packets, quizzes, prelabs, labs, practice exams, or lecture ACTs should be considered fair game for the exam. Also, I would advise not becoming too dependent on the equation sheet during your studying. It has valuable information on it, but it provides this information without context. It is much better to have a solid understanding of the concepts and the derivations which stand behind the equations, because then you can easily handle unfamiliar problems, or derive the correct equation for your purposes on the fly. Okay, rant over. 2 Everyday waves: the wave equation 2.1 Basics Many of the waves we see in the everyday world and use as little toy physics lab problems can be described by a relatively “simple” differential equation called the wave equation. This equation describes a disturbance Ψ( x, t ) whose size varies depending on where and when you measure it, and is commonly written as follows: 2 Ψ ∂x 2 = 1 v 2 2 Ψ ∂t 2 (1) (Don’t be intimidated by the ∂/∂x things if you haven’t seen them before — they just mean you should take the derivative of the function Ψ only with respect to, eg. , x , and treat all other variables, such as t , as if they were constant. So if Ψ( x, t ) = 3 x + 4 t then Ψ /∂x = 3 and Ψ /∂t = 4.) The parameter v is a constant and is usually computed from the specific characteristics of the system in question. Examples of systems which satisfy this wave equation include waves on a string, sound waves, and light waves (also known as photons).
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