Physics: Wave-Particle Duality and Effects

Wave Particle Duality

• Light exhibits both wave-like and particle-like properties
• Demonstrated by phenomena such as interference, diffraction, and the photoelectric effect
• Particles can also exhibit wave-like properties as described by de Broglie's hypothesis
• The wavelength of a particle is inversely proportional to its momentum

Compton Effect And Photoelectric Effect

• Compton Effect: A phenomenon where X-rays scatter off electrons, resulting in a decrease in their energy
• Photoelectric Effect: The emission of electrons from a material when light shines on it
• Both effects provide evidence for the particle nature of light, as they can be explained by the interaction of photons with electrons

Uncertainty Principle

• Introduced by Werner Heisenberg
• States that it is impossible to simultaneously know both the momentum and position of a particle with perfect accuracy
• The product of the uncertainties in position and momentum is always greater than or equal to a constant value (Planck's constant divided by 4π)

Probability Current Density

• Represents the probability of finding a particle at a given point in space
• It's defined as the rate of change of probability density over time
• It can be used to describe the motion of particles in quantum mechanics

Expectation Values

• Represents the average value of a physical quantity in a quantum system
• Calculated by integrating the product of the wave function, the operator representing the quantity, and the complex conjugate of the wave function
• Provides information about the probable value of the physical quantity

Free-particle Wave Function And Wave-packets

• Free Particle: A particle that is not subject to any external forces
• Wave Function: A mathematical function that describes the state of a quantum particle
• Wave-packets: Localized wave functions formed by the superposition of different waves
• Free-particle wave functions exhibit both wave-like and particle-like behaviors

Time-dependent And Time-independent Schrodinger Equation

• Time-dependent Schrodinger Equation: Describes the evolution of a quantum system over time
• Time-independent Schrodinger Equation: Describes the stationary states of a quantum system, whose wave function doesn't change over time
• Both equations are fundamental to understanding the behavior of quantum particles and are used to solve various problems in quantum mechanics