Answered: Section 5.10 Exploring the uncertainty…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Q1. Consider the finite square well potential shown in the following diagram: U(x) E>0 L The potential is given by: for xL| -U. for 0 0is incident on this region from the left. Using the plane A particle with energy wave approximation for the particle: a) Show that Y = Ae*+Be¬k* is a suitable general solution to the time-independent Schrödinger wave-equation (TISE) that applies in the region x L write down the four equations arising from the boundary conditions that apply at x=0 and x=L .
3. Plane waves and wave packets. In class, we solved the Schrodinger equation for a "free particle" (e.g. when U(x,t) = 0). The correct[solution is (x, t) = Ae(px-Et)/ħ This represents a "plane wave" that exists for all x. However, there is a strange problem with this: if you try to normalize the wave function (determine A by integrating * for all x), you will find an inconsistency (A has to be set equal to 0?). This is because the plane wave stretches to infinity. In order to actually represent a free particle, this solution needs to be handled carefully. Explain in words (and/or diagrams) how we can construct a "wave packet" from the plane wave solution. (Hint 1: consider a superposition of plane waves for a limited range of momentum/energy. Hint 2: have a look at the brief discussion in the middle of pg. 278 and especially pg. 308-309 of the text.)
Subject Quantum Mechanics. Wave function normalization and superposition of solutions. Wavel functions, ψ1 and ψ2 both normalized. Find a relationship between A and B such that the superposition Aψ1 + Bψ2 is also a normalized solution. I'm having trouble with the integral of |Aψ1 + Bψ2|2 dx. Thank you!

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Section 5.10 Exploring the uncertainty principle 0.00 Function: Y(x)=y(A) + 2(x) Time: -10.00 5.00 5.00 0.00 Two waves: set values Wave packet: set values