5. (McQuarrie 3-27) Calculate (p) and (p2) for the n = 2 state of a particle in a 1-D box of length a. Show that: ор = h a What happens to your uncertainty in the momentum as the box size shrinks? Relate this to the Heisenberg uncertainty principle. 7. (McQuarrie 3-30) Show that the normalized wave function for a particle in a 3-D box with sides of length a, b, and c is: P(x, y, z) = √ √ sin ("") sin ("") sin ("-2) 8 abc a пупу b Hint: You can argue the form of the solution based on separation of variables and the known 1-D solutions. Then just show that the resulting 3-D wave function is normalized.
5. (McQuarrie 3-27) Calculate (p) and (p2) for the n = 2 state of a particle in a 1-D box of length a. Show that: ор = h a What happens to your uncertainty in the momentum as the box size shrinks? Relate this to the Heisenberg uncertainty principle. 7. (McQuarrie 3-30) Show that the normalized wave function for a particle in a 3-D box with sides of length a, b, and c is: P(x, y, z) = √ √ sin ("") sin ("") sin ("-2) 8 abc a пупу b Hint: You can argue the form of the solution based on separation of variables and the known 1-D solutions. Then just show that the resulting 3-D wave function is normalized.
Principles of Modern Chemistry
8th Edition
ISBN:9781305079113
Author:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler
Publisher:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler
Chapter4: Introduction To Quantum Mechanics
Section: Chapter Questions
Problem 37P: (a) Using Equation 4.36, make a graph of the n=3 wave function and the square of this wave function...
Related questions
Question
please answer these questions!!
![5. (McQuarrie 3-27) Calculate (p) and (p2) for the n = 2 state of a particle in a 1-D box of
length a. Show that:
ор
=
h
a
What happens to your uncertainty in the momentum as the box size shrinks? Relate this to
the Heisenberg uncertainty principle.
7. (McQuarrie 3-30) Show that the normalized wave function for a particle in a 3-D box with
sides of length a, b, and c is:
P(x, y, z) = √ √ sin ("") sin ("") sin ("-2)
8
abc
a
пупу
b
Hint: You can argue the form of the solution based on separation of variables and the known
1-D solutions. Then just show that the resulting 3-D wave function is normalized.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9d7dc701-b654-4339-995f-9e7ccdd48dfe%2Fc8c3654b-e6c0-4f58-a038-32293eff383c%2F4me5g7y_processed.png&w=3840&q=75)
Transcribed Image Text:5. (McQuarrie 3-27) Calculate (p) and (p2) for the n = 2 state of a particle in a 1-D box of
length a. Show that:
ор
=
h
a
What happens to your uncertainty in the momentum as the box size shrinks? Relate this to
the Heisenberg uncertainty principle.
7. (McQuarrie 3-30) Show that the normalized wave function for a particle in a 3-D box with
sides of length a, b, and c is:
P(x, y, z) = √ √ sin ("") sin ("") sin ("-2)
8
abc
a
пупу
b
Hint: You can argue the form of the solution based on separation of variables and the known
1-D solutions. Then just show that the resulting 3-D wave function is normalized.
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