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Quantum entanglement is a phenomenon where quantum states of two or more objects are interdependent, such that the state of one cannot be fully described without the other, even when separated by large distances.

Quantum beats arise from the interference of two or more quantum states with different energies, resulting in a time-dependent fluctuation in the probability of finding the system in a particular state.

In the mathematical description of Young's double-slit experiment, the wave functions from the two slits superpose, and the resulting interference pattern intensity is given by $I(\theta)=I_0 \cos^2\left(\frac{\pi d \sin\theta}{\lambda}\right)$, where $\theta$ is the angle, $d$ is the slit separation, and $\lambda$ is the wavelength.

Coherence in quantum systems refers to a property of wave functions where their phase relation is well-defined, which is necessary for interference effects to be observed.

The path integral formulation of quantum mechanics, developed by Richard Feynman, uses the sum over histories approach for calculating quantum amplitudes, which inherently encompasses interference effects.

An interference pattern is the result of superposition of two or more waves, leading to regions of constructive and destructive interference that can be observed in experiments such as the double-slit.

The superposition principle states that a quantum system can exist in multiple states at once, and the observable result is a combination of the probabilities for different outcomes.

Decoherence describes the loss of coherence in a quantum system, usually due to interactions with the environment, which in turn diminishes interference effects and can lead to classical behavior.

In quantum systems, the phase difference between two wave functions determines the type of interference (constructive or destructive) that will occur when they overlap.

Wave-particle duality is the concept that all particles exhibit both wave and particle properties, with quantum interference highlighting the wave-like behavior as seen in interference patterns and diffraction.

Quantum superposition is the fundamental principle that allows a quantum system to be in a combination of multiple states simultaneously, leading to interference effects when measurements are made.

The wave function in quantum mechanics is a mathematical description of the quantum state of a system, capable of displaying interference effects when multiple wave functions overlap.

Quantum interference is the phenomenon where waves of quantum probability amplitudes for different possible events combine, reinforcing or cancelling each other like waves in classical physics.

The double-slit experiment demonstrates quantum interference by showing how particles like electrons exhibit wave-like behavior, creating an interference pattern on a detection screen after passing through two slits.