AVQM Energy Diagrams I - Advanced Visual Quantum Mechanics...

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Advanced Visual Quantum Mechanics – Energy Diagrams in One Dimension Part I 1. Introduction When you first began to learn physics, you probably learned to think about interactions in terms of forces. In your more advanced physics courses you have focused more on describing interactions in terms of energy. In quantum mechanics, the potential energy as a function of position appears explicitly in the main equation of motion, the Schrödinger Equation, so we use the concept of energy to describe all interactions. A convenient way to get a quick overview of a particle’s motions and interactions is with an energy diagram, a plot of the object’s potential, kinetic, and/or total energy versus its position. This interactive engagement is designed to help you remember what you know about using energy diagrams to describe physical situations. 1.1 The Roller Coaster At some time or another you have probably talked about energy in the context of a frictionless roller coaster. You have seen sketches of a track like figure 1.1a and discussed the potential and kinetic energy of a cart at various locations on the track. Figure 1.1a: A roller coaster track. Exercise 1.1a : Sketch the potential energy (V) as a function of position (x) for the situation shown in figure 1.1a. Assume that V=0 when y=0. In this case, the potential energy function versus x is exactly the same shape as the height (y) versus x because gravitational potential energy near the earth is proportional to height x y x V
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(V=mgy). But this situation can be somewhat confusing. Although the motion can be described with only one space dimension (x) and the potential energy can be written as a function of only one variable (x), the cart is actually moving in two dimensions (x and y). (The reason the situation can be described in one variable is because there is a constraint – the cart must remain on the track.) To avoid this confusion we will focus our attention on situations where the motion really is along a straight line. Exercise 1.1b : Describe an example of a physical situation where energy is conserved and a particle is moving along a straight line with a non-constant potential energy. Exercise 1.1c : Sketch a graph of the potential energy function for the situation you described in Exercise 1.1b. 2. Energy Diagrams for Cars on Tracks with Magnetic Interactions In the following activities you will study energy diagrams for toy cars moving on a track with magnetic interactions. In each part you will first study what happens when friction is present then you will think about what would happen if friction could be removed. In later activities you will use a computer program that can simulate the toy cars without any friction. 2.1 Energy Diagrams for No Magnetic Interactions
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This note was uploaded on 09/10/2009 for the course PHY 76875 taught by Professor Turner during the Summer '09 term at University of Texas at Austin.

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AVQM Energy Diagrams I - Advanced Visual Quantum Mechanics...

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