Thermal State Calculator
Enter the mean photon number. The Thermal State Calculator instantly computes variance, Mandel Q, g²(0), and all photon statistics for blackbody/thermal light.
About the Thermal State Calculator
The Thermal State Calculator is a precise, scientifically accurate tool that computes photon statistics for thermal (chaotic) light — the quantum description of blackbody radiation and classical noisy light sources. This Thermal State Calculator implements the exact Bose-Einstein distribution formulas for mean, variance, Mandel Q, and second-order coherence g²(0). Proudly supported by Agri Care Hub.
Scientific Definition
p_n = ⟨n⟩^n / (1 + ⟨n⟩)^(n+1)
⟨n⟩ = mean photon number
Variance = ⟨n⟩(⟨n⟩ + 1)
Q = ⟨n⟩ (super-Poissonian)
g²(0) = 2 (photon bunching)
Why This Calculator Is Essential
Thermal states describe: • Blackbody radiation and starlight • Chaotic light from LEDs, lamps, sunlight • Hanbury Brown-Twiss experiments • Classical noise in optics • Benchmark for non-classical light detection They exhibit maximum classical noise (g²(0)=2) and super-Poissonian statistics.
How to Use
- Enter mean photon number ⟨n⟩ (from temperature or source).
- Click “Calculate Thermal State”.
- See variance, Q parameter, g²(0), and classification.
When Should You Use This Tool?
- Quantum optics and photon statistics
- Hanbury Brown-Twiss interferometry
- Thermal light source characterization
- Astrophysics and blackbody radiation
- Non-classical light verification
- Teaching classical vs quantum light
Scientific Foundation
Thermal states are the quantum analog of blackbody radiation, following Bose-Einstein statistics. They have maximum classical photon noise and bunching g²(0)=2. The variance ⟨n⟩(⟨n⟩+1) is twice the Poissonian value. Full theory at Thermal State on Wikipedia and Mandel & Wolf’s *Optical Coherence and Quantum Optics*.
Conclusion
The Thermal State Calculator brings the quantum statistics of blackbody radiation to your browser — with perfect accuracy and beautiful design. Whether you’re a student learning photon bunching, a researcher studying chaotic light, or an engineer characterizing thermal sources, this tool delivers precise results every time. For more quantum tools, visit Agri Care Hub.