Question
i) Write down the eigenfunctions for the and
states of the hydrogen atom.
ii) Write the eigenvalues of and
for the states
and
.
iii) Calculate the most probable value of r for the hydrogen atom in the state .
Answer :
Word Count : 188
For the hydrogen atom the stationary states are written as ψₙₗₘ(r,θ,φ)=Rₙₗ(r)Yₗₘ(θ,φ). i) For ψ₃₀₀ we have n=3, l=0, m=0. The angular part is the spherical harmonic Y₀₀(θ,φ)=1/√(4π). The radial part for _____ _________ ________ ________ ______.
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_______ ____ _______ ___ ________ _________ ________ ______ ________ ____.
____ ___ __________ _______ _______ _________ ____ _____.
_________ _______ __________ __________ __________ ____ ________.
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For the hydrogen atom the stationary states are written as ψₙₗₘ(r,θ,φ)=Rₙₗ(r)Yₗₘ(θ,φ). i) For ψ₃₀₀ we have n=3, l=0, m=0. The angular part is the spherical harmonic Y₀₀(θ,φ)=1/√(4π). The radial part for _____ _________ ________ ________ ______.
________ ____ ______ ____ _________ _________ _____ _______ _________ _____ _________ ____.
________ ______ __________ ______ ____.
___ _________ _____ _____ ___.
___ __________ ____ ________ _______ ___.
__________ ___ ___ __________ ______ ______ _______ _____.
_________ ______ ___ __________ _______ ___ _____ ________ ____ ________.
___ ___ _________ ________ ____ ___ _________ ___ _____.
_________ _____ _____ __________ _____ _______ _____.
_______ _____ _________ _________ ____ _____ ________ _____.
_________ ___ __________ ___ ____ ___ ____ _____ ____ _________.
_____ ____ _____ ________ ___ ___ ____ ________ __________ ___ ________.
______ ____ ___ _______ _______ __________.
____ ____ ___ ________ _______ ________ ____ ___ ____ ______.
__________ ____ ______ _________ __________ _________ _______ ______ __________ ________.
____ ____ __________ ______ ___ _________ ____ ________ ________ ____.
_______ ____ _______ ___ ________ _________ ________ ______ ________ ____.
____ ___ __________ _______ _______ _________ ____ _____.
_________ _______ __________ __________ __________ ____ ________.
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