Quantum Mechanics Intro
Quantum mechanics is a fundamental theory in physics that describes the behavior of matter and energy on microscopic scales, such as atoms and subatomic particles. Unlike classical mechanics, it relies on probability and wave functions rather than deterministic paths, introducing concepts like superposition and entanglement. This guide provides an introduction to quantum mechanics, covering all basic formulas (Planck’s equation, de Broglie relation, Schrödinger equation, Heisenberg uncertainty principle), detailed examples, and practical applications to illustrate its revolutionary impact on modern science and technology.
Planck’s Equation (with de Broglie, Schrödinger, Uncertainty)
Planck’s equation relates the energy of a photon to its frequency, marking the birth of quantum theory:
Where:
: Energy (J) : Planck’s constant : Frequency (Hz)
Related Formulas:
- de Broglie Relation:
, where (momentum) - Schrödinger Equation (Time-Independent, 1D):
(simplified, ) - Heisenberg Uncertainty Principle:
Examples
Example 1: Planck’s Equation
Energy of a photon with
Example 2: de Broglie Wavelength
Wavelength of an electron with mass
Example 3: Schrödinger Equation (Energy Estimate)
For a particle in a box (
Example 4: Heisenberg Uncertainty Principle
Minimum uncertainty in position if momentum uncertainty
Applications
Quantum mechanics drives modern technology and scientific advancements. Below are examples with calculations:
Example 1: Semiconductor Energy Levels
Energy of an electron in a quantum well (
Example 2: Laser Photon Energy
Energy of a photon from a laser with
Example 3: Electron Diffraction
Wavelength of an electron with
Example 4: Quantum Computing (Uncertainty)
Minimum position uncertainty if
Example 5: Atomic Transition Energy
Energy of a photon with
Example 6: Particle in a Box (Higher State)
Energy for