1. Consider the state referred to in the notes as the px orbital, 1 v (0, ¢) = (Y1,-1(0, 6) + Y1,1 (0, ¢)) V2 where Yım (0, ¢) are the spherical harmonics, as defined in the notes. a) Calculate the expectation values (L2) and (L²) in this state. b) Suppose L, was measured? What values could get, and with what probabili- ties? c) Is the quantum number associated with Lz good in this state? d) Calculate the expectation values (Lª) and (L²) in this state. e) Is the quantum number associated with L, good in this state? f) Calculate the expectation values (L,) and (L²) in this state. g) Is the quantum number associated with Ly good in this state? h) Confirm your answers above by explicitly showing which of Lx,y,z (if any) this state is an eigenfunction of, and finding the associated eigenvalue.
1. Consider the state referred to in the notes as the px orbital, 1 v (0, ¢) = (Y1,-1(0, 6) + Y1,1 (0, ¢)) V2 where Yım (0, ¢) are the spherical harmonics, as defined in the notes. a) Calculate the expectation values (L2) and (L²) in this state. b) Suppose L, was measured? What values could get, and with what probabili- ties? c) Is the quantum number associated with Lz good in this state? d) Calculate the expectation values (Lª) and (L²) in this state. e) Is the quantum number associated with L, good in this state? f) Calculate the expectation values (L,) and (L²) in this state. g) Is the quantum number associated with Ly good in this state? h) Confirm your answers above by explicitly showing which of Lx,y,z (if any) this state is an eigenfunction of, and finding the associated eigenvalue.
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 61AP: A particle of mass m is placed in a three-dimensional rectangular box with edge lengths 2L, L, and...
Related questions
Concept explainers
Atomic Structure
The basic structure of an atom is defined as the component-level of atomic structure of an atom. Precisely speaking an atom consists of three major subatomic particles which are protons, neutrons, and electrons. Many theories have been stated for explaining the structure of an atom.
Shape of the D Orbital
Shapes of orbitals are an approximate representation of boundaries in space for finding electrons occupied in that respective orbital. D orbitals are known to have a clover leaf shape or dumbbell inside where electrons can be found.
Question
Transcribed Image Text:1. Consider the state referred to in the notes as the px orbital,
1
v (0, ¢) = (Y1,-1(0, 6) + Y1,1 (0, ¢))
V2
where Yım (0, ¢) are the spherical harmonics, as defined in the notes.
a) Calculate the expectation values (L2) and (L²) in this state.
b) Suppose L, was measured? What values could get, and with what probabili-
ties?
c) Is the quantum number associated with Lz good in this state?
d) Calculate the expectation values (Lª) and (L²) in this state.
e) Is the quantum number associated with L, good in this state?
f) Calculate the expectation values (L,) and (L²) in this state.
g) Is the quantum number associated with Ly good in this state?
h) Confirm your answers above by explicitly showing which of Lx,y,z (if any) this
state is an eigenfunction of, and finding the associated eigenvalue.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 5 steps with 5 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.Recommended textbooks for you
Principles of Modern Chemistry
Chemistry
ISBN:
9781305079113
Author:
David W. Oxtoby, H. Pat Gillis, Laurie J. Butler
Publisher:
Cengage Learning
Introductory Chemistry: A Foundation
Chemistry
ISBN:
9781337399425
Author:
Steven S. Zumdahl, Donald J. DeCoste
Publisher:
Cengage Learning
Physical Chemistry
Chemistry
ISBN:
9781133958437
Author:
Ball, David W. (david Warren), BAER, Tomas
Publisher:
Wadsworth Cengage Learning,
Principles of Modern Chemistry
Chemistry
ISBN:
9781305079113
Author:
David W. Oxtoby, H. Pat Gillis, Laurie J. Butler
Publisher:
Cengage Learning
Introductory Chemistry: A Foundation
Chemistry
ISBN:
9781337399425
Author:
Steven S. Zumdahl, Donald J. DeCoste
Publisher:
Cengage Learning
Physical Chemistry
Chemistry
ISBN:
9781133958437
Author:
Ball, David W. (david Warren), BAER, Tomas
Publisher:
Wadsworth Cengage Learning,
Chemistry: An Atoms First Approach
Chemistry
ISBN:
9781305079243
Author:
Steven S. Zumdahl, Susan A. Zumdahl
Publisher:
Cengage Learning
Chemistry
Chemistry
ISBN:
9781305957404
Author:
Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:
Cengage Learning