The time-dependent Schrödinger equation describes how the quantum state of a physical system changes over time, encapsulating the dynamics of quantum mechanics. It is a fundamental equation that governs the evolution of wave functions, providing a bridge between quantum mechanics and classical mechanics through the concept of wave-particle duality.

Time-dependent Schrödinger Equation

A quantum state is a mathematical object that fully describes a quantum system, encapsulating all its possible information, such as position, momentum, and spin. It is typically represented by a wave function or a state vector in a complex Hilbert space, and its evolution is governed by the Schrödinger equation.

Quantum State

Physical System

Dynamics of quantum mechanics

Fundamental equation

Evolution of wave functions

Quantum mechanics is a fundamental theory in physics that describes the physical properties of nature at the smallest scales, such as atoms and subatomic particles. It introduces concepts like wave-particle duality, uncertainty principle, and quantum entanglement, which challenge classical intuitions about the behavior of matter and energy.

Quantum Mechanics

Classical mechanics is a branch of physics that deals with the motion of bodies under the influence of force, providing a framework for understanding the physical world from the macroscopic to the astronomical scale. It is based on principles such as Newton's laws of motion and the conservation of energy, serving as the foundation for more advanced theories like quantum mechanics and relativity.

Classical Mechanics

Wave-particle duality is a fundamental concept in quantum mechanics that describes how every particle or quantum entity exhibits both wave and particle properties. This duality is exemplified by experiments such as the double-slit experiment, where particles like electrons create interference patterns, a characteristic of waves, yet also behave as discrete particles when observed.

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