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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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View Full Document (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 nonconstant 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.
 Summer '09
 Turner
 Energy, Force

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