Quantum Foundations: 17 flashcards

The failure of classical physics (Rayleigh-Jeans law) to predict black body radiation at short wavelengths, predicting infinite energy as wavelength approaches zero.

An idealized object that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence.

That energy is quantized and emitted or absorbed in discrete packets (quanta) with energy $E = h\nu$, where $h$ is Planck's constant and $\nu$ is frequency.

$$u(\nu, T) = \frac{8\pi h \nu^3}{c^3} \frac{1}{e^{h\nu/(kT)} - 1}$$ where $u$ is energy density per unit frequency, $h$ is Planck's constant, $\nu$ is frequency, $c$ is speed of light, $k$ is Boltzmann constant, $T$ is temperature.

The emission of electrons from a metal surface when light of sufficient frequency shines on it.

Classical wave theory predicted that the kinetic energy of emitted electrons should increase with light intensity, and that any frequency of light could eject electrons given enough time. Experimentally, no electrons are emitted below a threshold frequency, and kinetic energy depends on frequency, not intensity.

The minimum energy required to eject an electron from a metal surface.

$$h\nu = \phi + K_{\text{max}}$$ where $h\nu$ is photon energy, $\phi$ is work function, and $K_{\text{max}}$ is maximum kinetic energy of emitted electrons.

The increase in wavelength (decrease in energy) of X-rays when they scatter off free electrons, demonstrating particle-like behavior of photons.

$$\Delta \lambda = \lambda' - \lambda = \frac{h}{m_e c}(1 - \cos\theta)$$ where $\Delta \lambda$ is the shift, $h$ is Planck's constant, $m_e$ is electron mass, $c$ is speed of light, $\theta$ is scattering angle.

That all matter exhibits wave-like behavior, with a wavelength given by $\lambda = \frac{h}{p}$, where $p$ is momentum.

$$\lambda = \frac{h}{p} = \frac{h}{mv}$$ for non-relativistic particles.

It established wave-particle duality for matter, leading to the development of wave mechanics and the Schrödinger equation.

Electron diffraction experiments (e.g., Davisson-Germer experiment) showing interference patterns consistent with wave behavior.

The concept that every quantum entity exhibits both wave and particle properties, depending on the experimental context.

A fundamental physical constant that relates the energy of a photon to its frequency: $E = h\nu$. Its value is approximately $6.626 \times 10^{-34} \text{ J s}$.

By quantizing energy, the Rayleigh-Jeans law is modified at high frequencies, suppressing the divergence and matching experimental black body spectra.