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6.1
The Schrödinger Wave Equation
6.2
Expectation Values
6.3
Infinite SquareWell Potential
6.4
Finite SquareWell Potential
6.5
ThreeDimensional Infinite
Potential Well
6.6
Simple Harmonic Oscillator
6.7
Barriers and Tunneling
CHAPTER 6
Quantum Mechanics II
Erwin Schrödinger (18871961)
Problem set 7, due March 14th :
Chapter 6: 5, 8, 10, 12, 15, 22, 23, 30, 31, 33
Keep reading carefully Chapter 6: there is a lot of important information in here.
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View Full Document 6.3: Infinite SquareWell Potential
The simplest such system is that of a particle
trapped in a box with infinitely hard walls that
the particle cannot penetrate. This potential is
called an infinite square well and is given by:
Clearly the wave function must be zero where the potential is infinite.
Where the potential is zero (inside the box), the timeindependent
Schrödinger wave equation becomes:
The general solution is:
x
0
L
wher
e
The energy is entirely kinetic
and so is positive.
Boundary conditions of the potential dictate
that the wave function must be zero at
x
= 0
and
x
=
L
. This yields valid solutions for
integer values of
n
such that
kL
=
n
π
.
The wave function is:
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This note was uploaded on 04/23/2011 for the course PHYS 342 taught by Professor Staff during the Spring '08 term at Purdue University.
 Spring '08
 Staff
 mechanics

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