Physics:Quantum Spectral lines and series

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Spectral lines are discrete wavelengths of light emitted or absorbed by atoms and molecules, arising from transitions between quantized energy levels, and they provided some of the earliest direct evidence for quantum theory.

Spectral lines arise from discrete electronic transitions in atoms, forming characteristic series such as Lyman, Balmer, and Paschen.

Origin of spectral lines

In quantum mechanics, electrons in atoms occupy discrete energy eigenstates. When an electron transitions between two states, a photon is emitted or absorbed with energy given by:

$E=h\nu =E_i-E_f$

where:

• $h$ is Planck’s constant
• $\nu$ is the frequency of the radiation
• $E_i$, $E_f$ are the initial and final energy levels

This leads to sharply defined spectral lines rather than a continuous spectrum.

Hydrogen spectral series

The hydrogen atom provides the simplest and most important example of spectral line structure. Its energy levels are given by:

$E_n=-\frac{13.6\text{ eV}}{n^2}$

Transitions between these levels produce series of spectral lines described by the Rydberg formula:

$\frac{1}{\lambda }=R(\frac{1}{n_f^2}-\frac{1}{n_i^2})$

where:

• $R$ is the Rydberg constant
• $n_i>n_f$

This relation accurately predicts observed hydrogen spectral lines.

Major series

• Lyman series ($n_f=1$) – ultraviolet region
• Balmer series ($n_f=2$) – visible region
• Paschen series ($n_f=3$) – infrared region
• Brackett series ($n_f=4$) – infrared
• Pfund series ($n_f=5$) – far infrared

Each series corresponds to transitions ending at a fixed lower energy level.

Fine structure and splitting

Real spectral lines are not perfectly sharp. They exhibit splitting due to additional physical effects:

• Fine structure — relativistic corrections and spin–orbit coupling
• Zeeman effect — splitting in an external magnetic field
• Stark effect — splitting in an electric field

These effects reveal deeper structure in atomic energy levels.

Selection rules

Not all transitions are allowed. Selection rules determine which spectral lines appear:

• $\mathrm{\Delta }l=\pm 1$
• $\mathrm{\Delta }m=0,\pm 1$

These arise from conservation of angular momentum and symmetry properties of atomic wavefunctions.

Spectroscopy and applications

Spectral lines are fundamental in many areas of physics and astronomy:

• Identifying chemical elements in stars and galaxies
• Measuring Doppler shifts and cosmic expansion
• Determining temperatures and densities of plasmas
• Laser technology and atomic clocks

Each element has a unique spectral “fingerprint.”

Table of content (70 articles)

Core pathway

1. Physics:Quantum basics
2. Physics:Quantum mechanics
3. Physics:Quantum mechanics measurements
4. Physics:Quantum Interpretations of quantum mechanics
5. Physics:Quantum Mathematical Foundations of Quantum Theory
6. Physics:Quantum Atomic structure and spectroscopy
7. Physics:Quantum Density matrix
8. Physics:Quantum Open systems
9. Physics:Quantum Statistical mechanics
10. Physics:Quantum Kinetic theory
11. Physics:Plasma physics (fusion context)
12. Physics:Tokamak physics
13. Physics:Tokamak edge physics and recycling asymmetries

Full contents

Foundations

1. Physics:Quantum basics
2. Physics:Quantum mechanics
3. Physics:Quantum mechanics measurements
4. Physics:Quantum Mathematical Foundations of Quantum Theory

Conceptual and interpretations

5. Physics:Quantum Interpretations of quantum mechanics
6. Physics:Quantum A Spooky Action at a Distance
7. Physics:Quantum A Walk Through the Universe
8. Physics:Quantum: The Secret of Cohesion: How Waves Hold Matter Together

Mathematical structure and systems

9. Physics:Quantum Density matrix
10. Physics:Quantum Exactly solvable quantum systems
11. Physics:Quantum Formulas Collection
12. Physics:Quantum A Matter Of Size
13. Physics:Quantum Symmetry in quantum mechanics
14. Physics:Quantum Angular momentum operator
15. Physics:Runge–Lenz vector
16. Physics:Quantum Approximation Methods
17. Physics:Quantum Matter Elements and Particles

Atomic and spectroscopy

18. Physics:Quantum Atomic structure and spectroscopy
19. Physics:Quantum Hydrogen atom
20. Physics:Quantum Selection rules
21. Physics:Quantum Fermi's golden rule
22. Physics:Quantum Spectral lines and series

Wavefunctions and modes

23. Physics:Quantum Wavefunction
24. Physics:Quantum Superposition principle
25. Physics:Quantum Eigenstates and eigenvalues
26. Physics:Quantum Boundary conditions and quantization
27. Physics:Quantum Standing waves and modes
28. Physics:Quantum Normal modes and field quantization
29. Physics:Number of independent spatial modes in a spherical volume
30. Physics:Quantum Density of states

Quantum information and computing

31. Physics:Quantum information theory
32. Physics:Quantum Qubit
33. Physics:Quantum Entanglement
34. Physics:Quantum Gates and circuits
35. Physics:Quantum Computing Algorithms in the NISQ Era
36. Physics:Quantum Noisy Qubits

Quantum optics and experiments

37. Physics:Quantum Nonlinear King plot anomaly in calcium isotope spectroscopy
38. Physics:Quantum optics beam splitter experiments
39. Physics:Quantum Ultra fast lasers
40. Physics:Quantum Experimental quantum physics
41. Template:Quantum optics operators

Open quantum systems

42. Physics:Quantum Open systems
43. Physics:Quantum Master equation
44. Physics:Quantum Lindblad equation
45. Physics:Quantum Decoherence
46. Physics:Quantum Markovian dynamics
47. Physics:Quantum Non-Markovian dynamics
48. Physics:Quantum Trajectories

Quantum field theory

49. Physics:Quantum field theory (QFT) basics
50. Physics:Quantum field theory (QFT) core

Statistical mechanics and kinetic theory



51. Physics:Quantum Statistical mechanics
52. Physics:Quantum Partition function
53. Physics:Quantum Distribution functions
54. Physics:Quantum Liouville equation
55. Physics:Quantum Kinetic theory
56. Physics:Quantum Boltzmann equation
57. Physics:Quantum BBGKY hierarchy
58. Physics:Quantum Transport theory
59. Physics:Quantum Relaxation and thermalization

Plasma and fusion physics

60. Physics:Plasma physics (fusion context)
61. Physics:Tokamak physics
62. Physics:Tokamak edge physics and recycling asymmetries
• Hierarchy of modern physics models showing the progression from quantum statistical mechanics to kinetic theory and plasma physics, culminating in tokamak edge transport and recycling asymmetries.

Timeline

63. Physics:Quantum mechanics/Timeline
64. Physics:Quantum_mechanics/Timeline/Quiz/

Advanced and frontier topics

65. Physics:Quantum Supersymmetry
66. Physics:Quantum Black hole thermodynamics
67. Physics:Quantum Holographic principle
68. Physics:Quantum gravity
69. Physics:Quantum De Sitter invariant special relativity
70. Physics:Quantum Doubly special relativity

References

Author: Harold Foppele