Quantum Physics

Overview

Quantum Physics is the branch of physics that deals with the behavior of particles on atomic and subatomic scales. It introduces concepts such as quantization of energy, wave-particle duality, uncertainty principle, and quantum entanglement.

Key Concepts

Wave-Particle Duality

Particles like electrons exhibit both wave and particle properties.

Uncertainty Principle

It is impossible to know both the position and momentum of a particle with complete certainty.

Quantum Superposition

A particle can exist in multiple states simultaneously until measured.

Quantum Tunneling

Particles can pass through potential barriers that would be impossible in classical physics.

Important Equations

E = hf

Energy of a photon is proportional to its frequency. (Planck's relation)

λ = h/p

de Broglie wavelength: Wave nature of particles where h is Planck’s constant and p is momentum.

Δx · Δp ≥ ℏ / 2

Heisenberg Uncertainty Principle: Limitation on simultaneous measurement of position and momentum.

Ψ² = Probability Density

The square of the wave function gives the probability of finding a particle.

Applications

Example Problems

1. Find the energy of a photon with frequency 6×10¹⁴ Hz.

Solution: E = hf = 6.63×10⁻³⁴ × 6×10¹⁴ = 3.978×10⁻¹⁹ J

2. Calculate the de Broglie wavelength of a 1 kg object moving at 1 m/s.

Solution: λ = h/p = 6.63×10⁻³⁴ / 1 = 6.63×10⁻³⁴ m

3. If Δx = 1×10⁻¹⁰ m, what is the minimum Δp?

Solution: Δp ≥ ℏ / 2Δx = (1.055×10⁻³⁴) / (2×10⁻¹⁰) = 5.28×10⁻²⁵ kg·m/s