Quantum Numbers for Hydrogen Atom Electron

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SUMMARY

The quantum numbers required to specify the state of an electron in a hydrogen atom include the principal quantum number (n), total orbital angular momentum quantum number (l), magnetic quantum number (ml), total spin quantum number (s), and spin magnetic quantum number (ms). For a hydrogen atom with no angular dependence in its spatial wavefunction, the values are l = 0 and ml = 0, indicating a spherically symmetric state. The principal quantum number n is related to the radial part of the wavefunction and cannot be determined solely from the angular momentum quantum numbers. The total spin quantum number s is fixed at 1/2, while ms can take values of ±1/2.

PREREQUISITES
  • Understanding of quantum mechanics concepts, specifically quantum numbers.
  • Familiarity with the hydrogen atom model and its wavefunctions.
  • Knowledge of angular momentum in quantum systems.
  • Basic principles of electron spin and its quantization.
NEXT STEPS
  • Study the implications of quantum numbers in atomic structure.
  • Learn about the Schrödinger equation and its application to hydrogen atoms.
  • Explore the significance of the quantum numbers in determining electron configurations.
  • Investigate the role of angular momentum in quantum mechanics.
USEFUL FOR

Students of quantum mechanics, physicists studying atomic structure, and educators teaching advanced topics in quantum theory.

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Homework Statement



Define the quantum numbers required to specify the state of an electron in hydrogen. The spatial part of the wave-function describing a particular hydrogen atom has no angular dependence. Give the values of all the angular momentum quantum numbers for the electron.


Homework Equations





The Attempt at a Solution



so am i right that the numbers are:

n - the total energy quantum number, n = L+1 where L is max value of l
l - total orbital angular mom quant number
ml - z comp of orbital ang mom
s - total spin quantum number
ms - z comp of spin

what about the next part?

if the spatial wavefunction has no angular dependence then i guess that l = 0, ml = 0. We know that s = 1/2. What about ms and n? Surely these can't be known?
 
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hellooo people - should this be in advanced?
 

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