Explore quantum phenomena like wave-particle duality, uncertainty principle, and quantum tunneling through interactive visualizations and experiments.
Demonstrates wave-particle duality by showing how particles create an interference pattern when passing through two slits.
Quantum mechanics is a fundamental theory in physics that describes nature at the smallest scales of energy levels of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science.
One of the central concepts of quantum mechanics is wave-particle duality, which states that every particle or quantum entity may be described as either a particle or a wave. This duality addresses the inability of classical concepts like "particle" or "wave" to fully describe the behavior of quantum-scale objects.
The double-slit experiment demonstrates this duality. When particles like electrons or photons are sent through a double-slit apparatus one at a time, they create an interference pattern on the detector screen as if they were waves, even though they are detected as individual particles.
In quantum mechanics, the state of a system is described by a wave function (usually denoted as ψ), which is a mathematical function that provides information about the probability amplitude of position, momentum, and other physical properties of a particle.
The square of the absolute value of the wave function (|ψ|²) gives the probability density for finding the particle at a given point. This probabilistic interpretation is a core feature of quantum mechanics and represents a departure from the deterministic nature of classical physics.
The Schrödinger equation describes how the quantum state of a physical system changes over time:
Where ħ is the reduced Planck constant, i is the imaginary unit, and Ĥ is the Hamiltonian operator (which characterizes the total energy of the system).
Quantum tunneling is a quantum mechanical phenomenon where a particle passes through a potential energy barrier that it classically could not surmount. This plays an essential role in several physical phenomena, such as nuclear fusion in stars, radioactive decay, and certain types of chemical reactions.
The probability of tunneling depends on the height and width of the barrier, as well as the energy and mass of the particle. The tunneling probability can be approximated by:
Where k = √(2m(V-E))/ħ, m is the particle mass, V is the barrier height, E is the particle energy, and L is the barrier width.
The Heisenberg uncertainty principle states that there is a fundamental limit to the precision with which complementary variables (such as position and momentum) can be known simultaneously. Mathematically, it is expressed as:
Where Δx is the uncertainty in position, Δp is the uncertainty in momentum, and ħ is the reduced Planck constant.
This principle is not a statement about the limitations of measurement technology, but rather a fundamental property of quantum systems. It implies that the more precisely one property is measured, the less precisely the complementary property can be controlled or determined.
Quantum mechanics has led to numerous technological advancements and continues to be at the forefront of scientific research:
In this simulation, you can explore these fundamental quantum phenomena through interactive experiments that visualize the strange and counterintuitive behavior of quantum systems.