Quantum Phenomena Calculator

Because Photon Wavelength belongs to the Photoelectric Effect mode, not Quantum Tunneling -- the calculator only feeds the four tunneling inputs (Barrier Height, Barrier Width, Particle Energy, and Particle Mass) into the Transmission Coefficient formula. Switch the Phenomenon selector to "Photoelectric Effect" to see photon wavelength drive a result, specifically the ejected electron's maximum kinetic energy.

Barrier Height and Barrier Width, not Particle Mass or Particle Energy alone. Barrier Height sets V₀ in the exponential suppression term that governs how much of the particle's wavefunction survives crossing the barrier, and Barrier Width sets how much material that wavefunction has to tunnel through -- both appear directly inside the same exponential, which is why the transmission coefficient falls off so sharply as either one increases.

The Compton shift formula, Δλ = λc(1 − cos θ), factors out the electron's Compton wavelength (a fixed physical constant, about 2.43 picometers) from the angle-dependent term entirely -- the incident photon's own wavelength does not appear in the shift itself, only in the final wavelength (incident wavelength plus the shift). That is why the shift maxes out at exactly twice the Compton wavelength, at a 180° backscatter.

Yes, within the visible-light classification this calculator uses. Wien's displacement law puts the peak emission wavelength inversely proportional to temperature, so hotter objects peak at shorter (bluer) wavelengths -- the Sun's surface at 5,778 K peaks in visible green-yellow light, while a much hotter blue star's peak shifts into the ultraviolet, and a cooler object like a candle flame peaks in the infrared, below what the eye perceives as color at all.

The Quantum Entanglement mode largely reports the textbook properties of whichever Bell state and qubit count you select rather than computing them from a measured quantity -- the CHSH quantum bound (2√2, the Tsirelson bound) is a fixed mathematical result for any maximally entangled two-qubit state, and the maximum entanglement entropy depends only on how many qubits you split into two halves, not on a continuous input you can dial up or down.