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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.

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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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.
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.
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