Physic Labs

Quantum mechanics

The crisis of classical physics and the quantum hypothesis

Blackbody radiation and the photoelectric effect motivated energy quanta; light and matter display wave–particle duality.

Classical physics describes many phenomena very well, yet it encounters problems such as the blackbody spectrum and photoelectric effect. These observations require more than a small correction: they change how energy exchange and measurement outcomes are described at microscopic scales.

Ephoton=hν,pphoton=hλ,λdB=hpE_{\text{photon}}=h\nu,\qquad p_{\text{photon}}=\frac{h}{\lambda},\qquad \lambda_{\text{dB}}=\frac{h}{p}

Definition: Energy quantum

Planck introduced the constant hh in describing blackbody radiation; Einstein interpreted light as energy quanta hνh\nu. A material particle of momentum pp has de Broglie's wavelength h/ph/p. These relations connect measurable quantities; they do not mean a classical particle follows a definite path while spreading like a water wave.

Each detection is a localized dot, while accumulated events form an interference pattern. Open or close a slit and compare the corresponding probability distribution.

Wave–particle behavior in experiments

In a double-slit experiment, individual photons make localized detections on the screen; after many events, their distribution forms interference fringes. Available which-path information suppresses interference. Quantum theory predicts probabilities for outcomes; it does not claim that a photon splits into classical pieces.

Example: Electron wavelength

An electron has momentum p=1.00×10−24p=1.00\times10^{-24} kg·m/s. Find its de Broglie wavelength.

Solution

λ=h/p=6.626×10−34/(1.00×10−24)=6.63×10−10\lambda=h/p=6.626\times10^{-34}/(1.00\times10^{-24})=6.63\times10^{-10} m = 0.663 nm.

For a quantitative check, consider photons of frequency ν\nu in the photoelectric effect. Raising beam intensity increases the number of emitted electrons per second, but their maximum kinetic energy is set by frequency: Kmax⁡=hν−ϕK_{\max}=h\nu-\phi, where ϕ\phi is the work function. If hν<ϕh\nu<\phi, no electron is emitted even after a long wait. This differs from the classical expectation that energy arrives continuously in proportion to intensity. The constant hh sets the action scale; for a macroscopic object, its tiny value makes quantum wavelengths and level spacings too small to notice.

Quick check

What is the energy of a photon of frequency ν\nu?

What typically happens when which-path information is available in a double-slit experiment?

References

  1. P. A. M. Dirac (1958). The Principles of Quantum Mechanics