The radial part of the Schrödinger equation for the hydrogen atom Ze² ħ² d ƏR (r) ħ² l ( l + 1) 2pr² dr 2 + R(r) = ER(r) dr 2μr² -R(r) - ATE has eigenvalues that depend on only the principal quantum number, n. True False
The radial part of the Schrödinger equation for the hydrogen atom Ze² ħ² d ƏR (r) ħ² l ( l + 1) 2pr² dr 2 + R(r) = ER(r) dr 2μr² -R(r) - ATE has eigenvalues that depend on only the principal quantum number, n. True False
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Transcribed Image Text:The radial part of the Schrödinger equation for the hydrogen atom
д
ħ ² l ( l + 1 )
Ze²
240² or (2² (1)
2μr dr
ər
R(r) = ER(r)
2μr²
+
-R(r) –
Απε
has eigenvalues that depend on only the principal quantum number, n.
True
False
Expert Solution
Step 1
Given that The radial part of the Schrödinger equation for the hydrogen atom can be written in the form:
-h²/(2µr2)d²R(r)/dr² +[e²/(4πε₀r)-l(l+1)ħ²/(2µr²)]R(r) = ER(r)
where R(r) is the radial wave function, µ is the reduced mass of the electron-proton system, e is the elementary charge, ε₀ is the vacuum permittivity, l is the orbital quantum number, and E is the total energy of the system.
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