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Hydrogen atom in quantum mechanics
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Energy levels from the Schrödinger equation.
E_n = −13.6 eV/n²Solving the Schrödinger equation with a Coulomb potential gives E_n = −13.6 eV/n² and orbitals labelled by n, l, m. Fine structure and hyperfine splitting arise from relativistic and spin effects.
The 21 cm hydrogen line maps galaxies.
Degeneracy n² (without spin).
In more detail
The hydrogen atom is solved exactly in quantum mechanics, giving discrete energy levels and wavefunctions described by quantum numbers. The energy depends only on the principal quantum number n.
Real-world uses
- Hydrogen spectra are used to measure fundamental constants.
- Astronomers identify hydrogen in stars from its spectral lines.
- Astronomers and spectroscopists use the hydrogen energy levels to identify hydrogen lines in stars and nebulae.
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Frequently asked questions
Why do the energies depend only on n?
Because of the symmetry of the Coulomb potential, which gives a degeneracy in angular momentum.
What is the ground state energy?
About 13.6 eV below the ionisation threshold.
What does 13.6 eV mean?
It is the energy needed to remove the electron from a hydrogen atom in its ground state.
Related topics in Quantum Mechanics
Alpha decay as tunnelling · Quantum harmonic oscillator · Zero point energy · Quantum numbers · Atomic orbitals · Electron spin