You will answer this question by dragging and dropping elements from the list below into boxes. The elements below are colour-coded: you can only drop an element into a box with a matching colour. Please note that you may need to leave some of the boxes blank. Do not include any items that are equal to zero. The following wavefunction is a solution for the time-independent Schrödinger equation for a particle inside a one-dimensional finite potential energy barrier: y=A exp (-ax). (a) The particle has total energy E
You will answer this question by dragging and dropping elements from the list below into boxes. The elements below are colour-coded: you can only drop an element into a box with a matching colour. Please note that you may need to leave some of the boxes blank. Do not include any items that are equal to zero. The following wavefunction is a solution for the time-independent Schrödinger equation for a particle inside a one-dimensional finite potential energy barrier: y=A exp (-ax). (a) The particle has total energy E
Modern Physics
3rd Edition
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Chapter6: Quantum Mechanics In One Dimension
Section: Chapter Questions
Problem 29P
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Question
![You will answer this question by dragging and dropping elements from the list below into
boxes. The elements below are colour-coded: you can only drop an element into a box
with a matching colour. Please note that you may need to leave some of the boxes blank.
Do not include any items that are equal to zero.
The following wavefunction is a solution for the time-independent Schrödinger equation for
a particle inside a one-dimensional finite potential energy barrier:
y=A exp (-ax).
(a) The particle has total energy E<W, with W its potential energy inside the barrier.
Taking this into account, complete the Schrödinger equation below for the system under
consideration:
d²w 2m
dx-2
+
たこ
W = 0.
(b) In order to show that the wavefunction is indeed a solution of the Schrödinger
equation above, differentiate it twice with respect to the coordinate x and complete the
equation below:
dx
(c) Finally, introduce the above result into the Schrödinger equation and determine the
expression for a that is consistent with y being one of its solutions. Write this expression
using the boxes below:
+
α
E
W
x
sin
COS
sin2 cos² exp
Y
2m
h
h2
A
A²
α
d](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff3892faf-8df4-41bb-971d-190803d545bb%2F97bd6cf6-7a54-40c4-983f-55412260cb94%2Ftyqzhhc_processed.png&w=3840&q=75)
Transcribed Image Text:You will answer this question by dragging and dropping elements from the list below into
boxes. The elements below are colour-coded: you can only drop an element into a box
with a matching colour. Please note that you may need to leave some of the boxes blank.
Do not include any items that are equal to zero.
The following wavefunction is a solution for the time-independent Schrödinger equation for
a particle inside a one-dimensional finite potential energy barrier:
y=A exp (-ax).
(a) The particle has total energy E<W, with W its potential energy inside the barrier.
Taking this into account, complete the Schrödinger equation below for the system under
consideration:
d²w 2m
dx-2
+
たこ
W = 0.
(b) In order to show that the wavefunction is indeed a solution of the Schrödinger
equation above, differentiate it twice with respect to the coordinate x and complete the
equation below:
dx
(c) Finally, introduce the above result into the Schrödinger equation and determine the
expression for a that is consistent with y being one of its solutions. Write this expression
using the boxes below:
+
α
E
W
x
sin
COS
sin2 cos² exp
Y
2m
h
h2
A
A²
α
d
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