Question

An electron in Hydrogen atom is found to be in the state: |?? = R(r) [ 1/?3 Y1,0(?,?) ?+ + ?2/3 Y1,1(?,?) ?- ] Where: Y1,0 = ?3/(4?) cos ? and Y1,1 = - ?3/(8?) e^i? sin ? a) Calculate the expectation value of Jz. b) Show directly that the value of Jz is ?/2 and that the electron orbital angular momentum Lz is ?. c) What is the probability density of finding the electron with spin UP at r, ?, ??

          An electron in Hydrogen atom is found to be in the state:

|?? = R(r) [ 1/?3 Y1,0(?,?) ?+ + ?2/3 Y1,1(?,?) ?- ]

Where: Y1,0 = ?3/(4?) cos ? and Y1,1 = - ?3/(8?) e^i? sin ?

a) Calculate the expectation value of Jz.
b) Show directly that the value of Jz is ?/2 and that the electron orbital angular momentum Lz is ?.
c) What is the probability density of finding the electron with spin UP at r, ?, ??

An electron in Hydrogen atom is found to be in the state:

|?? = R(r) [ 1/?3 Y1,0(?,?) ?+ + ?2/3 Y1,1(?,?) ?- ]

Where: Y1,0 = ?3/(4?) cos ? and Y1,1 = - ?3/(8?) e^i? sin ?

a) Calculate the expectation value of Jz.
b) Show directly that the value of Jz is ?/2 and that the electron orbital angular momentum Lz is ?.
c) What is the probability density of finding the electron with spin UP at r, ?, ??

Added by Jasmin J.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Dominador Tan

01/18/2022

Step 1

In this case, the wave function is a superposition of two states, so we have to consider both terms. The operator Jz acts on the spherical harmonics Ylm, and its eigenvalues are mħ. Show more…

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An electron in Hydrogen atom is found to be in the state: |ψ⟩ = R(r) [ 1/√3 Y1,0(θ,φ) χ+ + √2/3 Y1,1(θ,φ) χ- ] Where: Y1,0 = √3/(4π) cos θ and Y1,1 = - √3/(8π) e^iφ sin θ a) Calculate the expectation value of Jz. b) Show directly that the value of Jz is ħ/2 and that the electron orbital angular momentum Lz is ħ. c) What is the probability density of finding the electron with spin UP at r, θ, φ?