Electromagnetic radiation behaves both as particles and waves, challenging our classical understanding of physics. This duality is key to grasping quantum mechanics, where light can act as discrete photons or spread out like waves, depending on how we observe it.

Quantum mechanics revolutionized our view of the microscopic world. It introduced probabilistic descriptions of nature, wave functions, and the uncertainty principle. These concepts help explain phenomena like electron orbitals and quantum tunneling, which classical physics couldn't account for.

The Particle-Wave Duality of Electromagnetic Radiation

Particle-wave duality of electromagnetic radiation

• Electromagnetic radiation exhibits both particle-like and wave-like properties
  • Particle-like properties
    • Photons are discrete packets or quanta of electromagnetic energy
    • Photon energy is given by $E = hf$, where $h$ is Planck's constant and $f$ is the frequency (visible light, X-rays)
  • Wave-like properties
    • Diffraction is the bending of light waves around obstacles or through openings (single-slit, double-slit)
    • Interference is the superposition of light waves, resulting in constructive and destructive interference patterns (thin films, soap bubbles)
• Implications for understanding light
  • Classical physics describes light as a wave
    • Explains phenomena like diffraction, interference, and polarization (wave theory of light)
  • Quantum physics describes light as particles (photons)
    • Explains phenomena like the photoelectric effect and Compton scattering (particle theory of light)
  • Complementarity principle states that both particle and wave descriptions are necessary for a complete understanding of light (wave-particle duality)

Challenges to classical physics

• Macroscopic objects appear to behave as either particles or waves
  • Particles are localized, follow definite trajectories, and interact through collisions (billiard balls, planets)
  • Waves spread out, exhibit diffraction and interference, and transfer energy without transferring matter (sound waves, water waves)
• Microscopic objects (photons, electrons) exhibit both particle and wave properties
  • Cannot be described solely as particles or waves
  • Behavior depends on the type of experiment or measurement performed (double-slit experiment)
• Challenges to classical intuition
  • Objects can behave as both particles and waves, depending on the context (complementarity)
  • The wave-particle duality is a fundamental aspect of quantum mechanics
  • Requires a shift in thinking from deterministic to probabilistic descriptions of nature (wave function, probability amplitudes)

Photons vs electrons

• Similarities between photons and electrons
  • Both exhibit particle-wave duality
  • Both can undergo diffraction and interference (double-slit experiment)
  • Both have a de Broglie wavelength given by $\lambda = h/p$, where $p$ is the momentum
• Differences between photons and electrons
  • Photons
    • Massless particles, always travel at the speed of light ($c$)
    • Carry electromagnetic force (mediate electromagnetic interactions)
    • Bosons: multiple photons can occupy the same quantum state (Bose-Einstein condensate)
  • Electrons
    • Massive particles, travel at speeds less than the speed of light ($v < c$)
    • Carry electric charge (negative charge, $-e$)
    • Fermions: subject to the Pauli exclusion principle, cannot occupy the same quantum state (atomic orbitals)
• Experimental evidence
  • Double-slit experiment: both photons and electrons create interference patterns
  • Photoelectric effect: photons behave as particles, ejecting electrons from a metal surface (work function, stopping potential)
  • Electron diffraction: electrons behave as waves, diffracting when passed through a crystal lattice (electron microscopy)

Quantum Mechanics and the Particle-Wave Duality

Quantum mechanics and the particle-wave duality

• Quantum mechanics is a fundamental theory describing the behavior of matter and energy at the atomic and subatomic scales
  • Developed to explain the particle-wave duality and other phenomena that classical physics could not account for (blackbody radiation, spectral lines)
  • Probabilistic description of nature: outcomes of measurements are inherently uncertain (quantum indeterminacy)
• Wave function is a mathematical description of a quantum system
  • Contains all the information about the system (state vector, Schrödinger equation)
  • Probability amplitude: square of the absolute value of the wave function gives the probability of finding a particle at a given location (Born rule)
• Measurement problem: the act of measurement affects the quantum system
  • Wave function collapse: a measurement causes the wave function to "collapse" into a definite state (Copenhagen interpretation)
  • Heisenberg uncertainty principle: the more precisely one property (position) is measured, the less precisely the complementary property (momentum) can be determined ($\Delta x \Delta p \geq \hbar/2$)

Matter waves and quantum superposition

• Matter waves: Louis de Broglie proposed that all matter exhibits wave-like properties
  • De Broglie wavelength: $\lambda = h/p$, where $h$ is Planck's constant and $p$ is momentum
  • Applies to all particles, including electrons, atoms, and even large molecules
• Quantum superposition: a fundamental principle of quantum mechanics
  • A quantum system can exist in multiple states simultaneously until measured
  • Explains phenomena such as electron orbitals and quantum tunneling
  • Leads to the concept of quantum entanglement and potential applications in quantum computing