3. A ID quantum well is described by the following position dependent potential energy for a moving particle of mass m: x<0, V = {-V, 0 L, where V, is a positive constant and L is the width of the quantum well. The total energy E of the particle is between -V, and 0 (i.e., -V, < E < 0 so bound states only!). Find the wavefunctions in each region. Apply as many boundary conditions as possible to these wavefunctions. Normalization of the wavefunctions is not required.

Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
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Chapter28: Quantum Physics
Section: Chapter Questions
Problem 47P
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3.
A ID quantum well is described by the following position dependent potential energy for a
moving particle of mass m:
x < 0,
V = {-V, 0<x<L,
(2)
x >L,
where V, is a positive constant and L is the width of the quantum well. The total energy E of the
particle is between -V, and 0 (i.e., -V, < E < 0 so bound states only!). Find the wavefunctions in
each region. Apply as many boundary conditions as possible to these wavefunctions. Normalization
of the wavefunctions is not required.
Transcribed Image Text:3. A ID quantum well is described by the following position dependent potential energy for a moving particle of mass m: x < 0, V = {-V, 0<x<L, (2) x >L, where V, is a positive constant and L is the width of the quantum well. The total energy E of the particle is between -V, and 0 (i.e., -V, < E < 0 so bound states only!). Find the wavefunctions in each region. Apply as many boundary conditions as possible to these wavefunctions. Normalization of the wavefunctions is not required.
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