Physics:Quantum Density of states

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Quantum density of states describes how many quantum states are available within a given energy interval. It is commonly written as $g(E)$, where $g(E)dE$ gives the number of states between $E$ and $E+dE$.

Density of states showing how the number of available quantum states varies with energy in a quantum system.

Definition

The density of states is a counting function in energy space. It becomes useful when individual quantum levels are so closely spaced that the spectrum can be treated as effectively continuous.

Origin from quantization

In confined systems, boundary conditions restrict wavefunctions to discrete standing-wave solutions. As the size of the system increases, these discrete levels become densely packed, and a continuous density-of-states description becomes appropriate.

Free-particle and solid-state picture

In the free-electron model, electrons are treated as particles in a three-dimensional box. Counting the allowed quantum states in momentum space leads to an energy-dependent density of states.

In solids, the available quantum states are organized into bands, and the density of states helps determine how electrons populate those bands.

Dependence on dimensionality

The density of states depends strongly on the dimensionality of the system:

• in one dimension, $g(E)$ decreases with energy
• in two dimensions, $g(E)$ is constant for an ideal free-particle system
• in three dimensions, $g(E)$ increases with $\sqrt{E}$

These differences are important in nanoscale systems such as quantum wells, wires, and dots.

Physical interpretation

The density of states tells how many quantum states are available at a given energy, but not whether they are occupied. Actual populations are determined only when the density of states is combined with a statistical distribution.

Applications

Density of states is fundamental in:

• solid-state physics
• semiconductor theory
• nanostructures and quantum wells
• statistical mechanics

It helps determine electrical, thermal, optical, and transport properties of materials.

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