Wave-Particle Duality Explained

Wave-particle duality is a fundamental principle of quantum mechanics that describes how every particle or quantum entity may be described as either a particle or a wave, depending on the context of the experiment.

De Broglie Wavelength

In 1924, Louis de Broglie proposed that all matter has wave properties. The wavelength of a particle is given by:

λ=hp=hmv\lambda = \frac{h}{p} = \frac{h}{mv}

where:

  • λ is the wavelength
  • h is Planck's constant
  • p is momentum
  • m is mass
  • v is velocity

Double-Slit Experiment

The double-slit experiment demonstrates wave-particle duality. When particles pass through two slits, they create an interference pattern characteristic of waves.

Wave Function

The wave function (ψ) describes the quantum state of an isolated system. The probability density is given by:

P(x)=∣ψ(x)∣2P(x) = |\psi(x)|^2

Key Equations

Energy of a Photon:

E=hf=hcλE = hf = \frac{hc}{\lambda}

Momentum of a Photon:

p=hλ=Ecp = \frac{h}{\lambda} = \frac{E}{c}

Schrödinger Wave Equation:

iℏ∂∂tΨ=−ℏ22m∇2Ψ+VΨi\hbar\frac{\partial}{\partial t}\Psi = -\frac{\hbar^2}{2m}\nabla^2\Psi + V\Psi