Computes the full interference pattern for two coherent sources: fringe spacing, path difference at any angle, intensity distribution, and coherence requirements. Accounts for finite slit width envelope modulation. Applicable to Young's experiment, acoustic interference, and microwave diffraction setups.
Full photoelectric analysis beyond the basic Einstein equation. Computes threshold frequency, stopping potential, maximum kinetic energy of emitted electrons, and photon flux. Supports work function input for any material. Useful for designing photoemission experiments and calibrating photomultiplier tubes.
// Output
Threshold frequency ν₀ and wavelength λ₀
Maximum KE of photoelectrons (eV and J)
Stopping potential V_s
Photon flux at given intensity
Quantum efficiency context
AETH-T02 · PHOTOEMISSION ENGINEACTIVE
Select material and incident frequency to analyse
03 · Matter Wave Physics
de Broglie Wavelength
Calculates the de Broglie wavelength for any particle with correct relativistic treatment for high-energy cases. Computes associated momentum, phase velocity, group velocity, and the thermal de Broglie wavelength at a given temperature — critical for assessing quantum degeneracy conditions in cold atom experiments and electron diffraction setups.
// Output
de Broglie wavelength λ_dB
Relativistic correction factor γ
Phase velocity v_ph
Thermal de Broglie wavelength at T
Quantum degeneracy condition
AETH-T03 · MATTER WAVE ENGINEACTIVE
Select particle and kinetic energy to compute
04 · Quantum Mechanics
Heisenberg Uncertainty Bounds
Computes both the position-momentum and energy-time uncertainty relations with physically meaningful interpretation. Given a measurement constraint on one observable, calculates the minimum uncertainty in the conjugate. Includes Robertson generalisation for arbitrary observables and the Kennard inequality for Gaussian wave packets.
// Output
Minimum Δp given Δx (and vice versa)
Minimum ΔE given Δt (and vice versa)
Gaussian wave packet spread over time
Physical interpretation of the bound
Comparison to classical limit
AETH-T04 · UNCERTAINTY ENGINEACTIVE
Select relation and input known uncertainty
05 · Quantum Mechanics
Quantum Tunneling Probability
Calculates the WKB transmission coefficient for a rectangular potential barrier. For E < V₀ gives the evanescent tunneling probability; for E > V₀ gives the resonance transmission with Ramsauer-Townsend oscillations. Critical for tunnel diode design, scanning tunnelling microscopy calibration, and nuclear alpha decay modelling.
// Output
Transmission coefficient T (WKB)
Reflection coefficient R = 1 − T
Decay constant κ (evanescent case)
Resonance condition (E > V₀ case)
Physical regime classification
AETH-T05 · TUNNELING ENGINEACTIVE
Enter barrier parameters to compute tunneling probability
06 · Thermal Physics
Blackbody Radiation Analysis
Full Planck distribution analysis: peak wavelength via Wien displacement, total radiated power via Stefan-Boltzmann, spectral radiance at arbitrary wavelength, and Rayleigh-Jeans comparison to quantify the ultraviolet catastrophe. Essential for stellar spectral classification, IR sensor calibration, and CMB analysis.
// Output
Peak wavelength λ_max (Wien's law)
Total power radiated per unit area
Spectral radiance B(λ,T) at given λ
Rayleigh-Jeans value (UV catastrophe ratio)
Stellar temperature classification
AETH-T06 · PLANCK ENGINEACTIVE
Sun: 5778 K · CMB: 2.725 K · Tungsten lamp: ~3200 K
Leave blank to compute only peak and total power
Enter temperature to analyse blackbody spectrum
07 · Atomic Physics
Hydrogen Spectroscopy
Computes energy levels, transition wavelengths, and spectral series for hydrogen and hydrogen-like ions using the Rydberg formula with reduced mass correction. Identifies spectral series (Lyman, Balmer, Paschen, Brackett, Pfund), computes fine structure splitting, and calculates the ionisation energy from any level.
// Output
Energy of levels n₁ and n₂ (eV)
Transition wavelength λ and frequency ν
Spectral series identification
Fine structure splitting ΔE_fs
Ionisation energy from n₁
AETH-T07 · SPECTROSCOPY ENGINEACTIVE
Enter quantum numbers to compute transition
08 · Semiconductor Physics
PN Junction Built-in Potential
Computes the built-in contact potential, depletion width, electric field profile, and capacitance of an abrupt PN junction at equilibrium and under applied bias. Includes both the one-sided and full depletion approximation. Essential for diode design, solar cell modelling, and MOSFET threshold voltage calculation.
// Output
Built-in potential V_bi
Depletion widths x_p, x_n, total W
Peak electric field E_max
Junction capacitance C_j per unit area
Breakdown field check
AETH-T08 · JUNCTION ENGINEACTIVE
Enter doping concentrations to analyse junction
09 · Semiconductor Physics
Carrier Concentration
Calculates intrinsic carrier concentration, Fermi level position, majority and minority carrier densities as a function of temperature and doping. Implements the complete Fermi-Dirac statistics with Joyce-Dixon approximation for degenerate semiconductors — not the simplified Boltzmann approximation that breaks down at high doping.
// Output
Intrinsic concentration n_i(T)
Fermi level E_F relative to midgap
Majority and minority carrier densities
Degeneracy check
Freeze-out temperature estimate
AETH-T09 · CARRIER ENGINEACTIVE
Select semiconductor and temperature to compute
10 · Electrodynamics
RLC Circuit Resonance Analysis
Complete analysis of series and parallel RLC circuits: resonant frequency, quality factor, bandwidth, impedance at arbitrary frequency, and phase angle. Computes the transient response regime (underdamped, critically damped, overdamped) and the 3dB bandwidth. Useful for filter design, RF matching network analysis, and oscillator characterisation.
// Output
Resonant frequency f₀ and ω₀
Quality factor Q
3dB bandwidth Δf
Impedance Z and phase φ at given f
Damping regime classification
AETH-T10 · RLC ENGINEACTIVE
Enter R, L, C values to analyse resonance
11 · Research Methodology
Uncertainty Propagation
Propagates measurement uncertainties through standard functional forms using both the quadrature (independent errors) and worst-case methods. Handles addition, subtraction, multiplication, division, powers, and logarithms. Outputs relative and absolute uncertainty with proper significant figures — the exact calculation every experimentalist does by hand before publication.
// Output
Absolute uncertainty δf
Relative uncertainty δf/f (%)
Dominant error source identified
Result with correct significant figures
Worst-case vs quadrature comparison
AETH-T11 · ERROR PROPAGATION ENGINEACTIVE
Enter measurement values and uncertainties
12 · Research Methodology
Experimental Data Statistics
Computes the full statistical profile of experimental datasets: mean, standard deviation, standard error of the mean, 95% confidence interval using t-distribution (correct for small samples), and a chi-squared goodness-of-fit test against a theoretical value. Identifies outliers via Grubbs test. What you'd otherwise compute in MATLAB or Python before writing up results.
// Output
Mean x̄ and median
Standard deviation σ and SEM
95% confidence interval (t-distribution)
Chi-squared test against theory
Grubbs outlier test
AETH-T12 · STATISTICS ENGINEACTIVE
Enter dataset to compute statistical profile
13 · Research Methodology
Dimensional Analysis Checker
Verifies dimensional consistency of physical equations by decomposing quantities into SI base dimensions [M, L, T, I, Θ, N, J]. Also performs Buckingham π theorem analysis: given a set of physical quantities, finds the dimensionless groups that govern the system — the first step in any scaling analysis or similitude study.
// Output
Dimensional decomposition of each quantity
Consistency check (pass / fail)
Buckingham π groups
Suggested dimensionless parameters
Common equation verification
AETH-T13 · DIMENSIONAL ENGINEACTIVE
Select equation to verify dimensional consistency
14 · Electrodynamics
EM Spectrum Complete Mapper
Converts between wavelength, frequency, wavenumber, photon energy, and equivalent temperature across the full electromagnetic spectrum. Identifies the spectral region and associated physical phenomena. Useful for spectroscopists, radio engineers, and anyone designing experiments involving electromagnetic radiation from ELF radio to gamma rays.
// Output
All representations (λ, ν, ν̃, E, T_equiv)
Spectral region identification
Typical sources in this region
Atmospheric transmission note
Detection technology used
AETH-T14 · SPECTRUM ENGINEACTIVE
Enter any EM quantity to map the full spectrum
15 · Optics
Diffraction Grating Spectrometer
Complete grating spectrometer analysis: diffraction angles for all orders, angular dispersion, resolving power, free spectral range, and blaze condition. Handles both transmission and reflection gratings with arbitrary blaze angle. Used in designing monochromators, spectrographs, and wavelength-division multiplexing systems.
// Output
Diffraction angles θ_m for orders m = 0,±1,±2,±3
Angular dispersion dθ/dλ
Chromatic resolving power R = λ/δλ
Free spectral range FSR
Blaze wavelength for given geometry
AETH-T15 · GRATING ENGINEACTIVE
Enter grating parameters to compute diffraction analysis
16 · Special Relativity
Lorentz Relativistic Effects
Computes the full suite of special relativistic effects: time dilation, length contraction, relativistic momentum and energy, velocity addition, and Doppler shift. Includes the rapidity formulation for composing boosts and the four-momentum invariant. Relevant for particle accelerator design, muon decay lifetime experiments, and GPS correction analysis.
// Output
Lorentz factor γ and rapidity φ
Time dilation Δt' and length contraction L'
Relativistic kinetic energy and total energy
Relativistic Doppler shift
Four-momentum invariant mass
AETH-T16 · RELATIVITY ENGINEACTIVE
Enter velocity (β) to compute relativistic effects
17 · Nuclear Physics
Radioactive Decay Analysis
Computes activity, remaining nuclei, and dose for single-isotope decay and two-member decay chains (secular and transient equilibrium). Finds the time of maximum daughter activity (Bateman equations). Outputs specific activity and Becquerel/Curie conversions. Used in nuclear medicine, radiation safety calculations, and radiometric dating.
// Output
Activity A(t) in Bq and Ci
Remaining fraction N(t)/N₀
Specific activity
Secular/transient equilibrium check
Time to reach daughter maximum (chain)
AETH-T17 · DECAY ENGINEACTIVE
Select isotope and enter parameters to compute decay
18 · Quantum Mechanics
Schrödinger Particle in a Box
Solves the 1D, 2D, and 3D infinite square well exactly: energy eigenvalues, degeneracy structure, transition wavelengths, and expectation values ⟨x⟩, ⟨x²⟩, ⟨p⟩, ⟨p²⟩. Also computes the finite square well bound states via transcendental equation. The canonical QM problem — but done properly with physical parameter inputs rather than arbitrary units.
// Output
Energy levels E_n (eV and J) for n = 1…6
Degeneracy of each level (2D/3D)
Transition wavelengths for Δn
⟨x⟩, ⟨p²⟩ = 2mE_n (uncertainty check)
Zero-point energy and its physical meaning
AETH-T18 · SCHRÖDINGER ENGINEACTIVE
Select geometry and box size to compute energy levels
19 · Condensed Matter Physics
Fermi Energy & Electron Gas
Computes the Fermi energy, Fermi temperature, Fermi velocity, and density of states at the Fermi level for a free electron gas. Calculates the temperature-dependent electronic heat capacity and chemical potential shift. Essential for understanding metallic behaviour, designing thermoelectric devices, and analysing degenerate semiconductors.
// Output
Fermi energy E_F (eV)
Fermi temperature T_F and velocity v_F
Density of states g(E_F)
Electronic heat capacity at T
Chemical potential shift μ(T) − E_F
AETH-T19 · FERMI ENGINEACTIVE
Select metal or enter electron density to compute
20 · Quantum Electrodynamics
Compton Scattering
Computes the Compton wavelength shift, scattered photon energy and momentum, recoil electron kinetic energy and direction for X-ray and gamma-ray scattering off free electrons. Includes the Klein-Nishina differential cross-section at the given angle — the relativistic QED correction to classical Thomson scattering that becomes significant above ~100 keV.
// Output
Wavelength shift Δλ = λ_c(1−cosθ)
Scattered photon energy E' and wavelength λ'
Recoil electron KE and angle φ
Klein-Nishina dσ/dΩ at given θ
Thomson vs Compton regime classification