


Lecture 10  Finite Square Well.pdf
Lecture_10__Finite_Square_Well.pdf
Showing 2935 out of 36
Lecture 10  Finite Square Well.pdfToday (1) Revi...
Lecture_10__Finite_Square_Well.pdfToday (1) Review of time dependent
Lecture 10  Finite Square Well.pdf...
Lecture_10__Finite_Square_Well.pdfToday (1) Review of time dependent
Page 29
29
wire
0
Energy
x
0
L
V(x)
Region I
Region II
Region III
)
(
)
(
)
(
)
(
2
2
2
2
x
E
x
x
V
dx
x
d
m
Need to solve Schrodinger Eqn:
4.7eV
E
electron
In Region II
…
total energy E > potential energy V
)
(
)
(
2
)
(
2
2
2
x
E
V
m
dx
x
d
Negative number
)
(
2
x
k
When E>V: Solutions = sin(kx), cos(kx), e
ikx
.
Always expect sinusoidal functions
k is real
Page 30
wire
0
Energy
x
0
L
V(x)
Region I
Region II
Region III
)
(
)
(
)
(
)
(
2
2
2
2
x
E
x
x
V
dx
x
d
m
Need to solve Schrodinger Eqn:
4.7eV
E
electron
In Region III
…
total energy E < potential energy V
)
(
)
(
2
)
(
2
2
2
x
E
V
m
dx
x
d
Positive
)
(
2
x
is real
What functional forms of
(x)
work?
a. e
i
x
b. sin(
x)
c. e
x
d. more than one of these
In class activity
30
Page 31
Answer is C: e
x
… could also be e

x
.
Exponential decay or growth
Why not e
i
x
?
)
(
)
(
2
2
x
x
LHS
RHS
wire
0
Energy
x
0
L
V(x)
Region I
Region II
Region III
)
(
)
(
)
(
)
(
2
2
2
2
x
E
x
x
V
dx
x
d
m
Need to solve Schrodinger Eqn:
4.7eV
E
electron
In Region III
…
total energy E < potential energy V
)
(
)
(
2
)
(
2
2
2
x
E
V
m
dx
x
d
Positive
)
(
2
x
is real
What functional forms of
(x)
work?
In class activity
31
Page 32
32
wire
0
Energy
x
0
L
V(x)
Region I
Region II
Region III
4.7eV
E
electron
x
x
III
Be
Ae
x
)
(
)
cos(
)
sin(
)
(
kx
D
kx
C
x
II
x
x
I
Fe
Ee
x
)
(
What will wave function in Region III look like?
What makes sense for constants A and B?
a. A must be 0
b. B must be 0
c. A and B must be equal
d. A=0 and B=0
e. A and B can be anything, need more info.
In class activity
Page 33
33
wire
0
Energy
x
0
L
V(x)
Region I
Region II
Region III
4.7eV
E
electron
x
x
III
Be
Ae
x
)
(
x
x
I
Fe
Ee
x
)
(
What will wave function in Region III look like?
What makes sense for constants A and B?
Answer is a.
A must be 0 .. otherwise
blows up as x gets bigger.
This doesn’t make sense!
and probability should
0 at large x!
Need to be able to normalize
)
cos(
)
sin(
)
(
kx
D
kx
C
x
II
Page 34
34
V=0 eV
0
L
4.7 eV
Energy
x
E
electron
x
III
Be
x
)
(
Inside well (E>V):
(Region II)
)
(
)
(
2
2
2
x
k
dx
x
d
II
II
)
(
)
(
2
2
2
x
dx
x
d
III
III
Outside well (E<V):
(Region III)
Boundary
Conditions:
continuous
)
(
L
continuous
)
(
dx
L
d
x
as
0
)
cos(
)
sin(
)
(
kx
D
kx
C
x
II
Outside well
(E<V):
(Region I)
On HW
next week
)
(
)
(
L
L
III
II
dx
L
d
dx
L
d
III
II
)
(
)
(
Page 35
35
V=0 eV
0
L
4.7 eV
Energy
x
E
electron
)
(
)
(
2
)
(
2
2
2
x
E
V
m
dx
x
d
Inside well (E>V):
Outside well (E<V):
Electron is delocalized … spread out.
Some small part of wave is where
Total energy is less than potential
energy!
“Classically forbidden”
region.
Ace your assessments! Get Better Grades
Browse thousands of Study Materials & Solutions from your Favorite Schools
UBC Vancouver
UBC_Vancouver
School:
Modern_Physics
Course:
Introducing Study Plan
Using AI Tools to Help you understand and remember your course concepts better and faster than any other resource.
Find the best videos to learn every concept in that course from Youtube and Tiktok without searching.
Save All Relavent Videos & Materials and access anytime and anywhere
Prepare Smart and Guarantee better grades
Students also viewed documents
lab 18.docx
lab_18.docx
Course
Course
3
Module5QuizSTA2023.d...
Module5QuizSTA2023.docx.docx
Course
Course
10
Week 7 Test Math302....
Week_7_Test_Math302.docx.docx
Course
Course
30
Chapter 1 Assigment ...
Chapter_1_Assigment_Questions.docx.docx
Course
Course
5
Week 4 tests.docx.do...
Week_4_tests.docx.docx
Course
Course
23
Week 6 tests.docx.do...
Week_6_tests.docx.docx
Course
Course
106