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Quantum Tunneling

Quantum tunneling is the phenomenon where particles can pass through potential barriers, even if they don't have enough energy to overcome them classically. This occurs due to the wave-like nature of matter.

The probability of tunneling depends on the barrier’s width and height, as well as the particle’s mass and energy. Smaller particles and thinner barriers lead to a higher probability of tunneling.

λ = h/p

Wave-Particle Duality

Wave-particle duality describes the concept that all matter exhibits properties of both waves and particles. This isn’t to say something is *both* a wave and a particle at the same time in the classical sense, but rather that it can exhibit characteristics of either depending on how it's observed.

Experiments like the double-slit experiment demonstrate this duality. Particles, such as electrons, can pass through two slits simultaneously, creating an interference pattern – a characteristic of waves. However, when individual particles are detected, they appear as localized events, consistent with particle behavior.

Ψ = c₁|ψ₁⟩ + c₂|ψ₂⟩

Non-Locality

Non-locality refers to the phenomenon where two entangled particles appear to influence each other instantaneously, regardless of the distance separating them.

This does not imply faster-than-light communication. The correlation arises from their shared quantum state established during entanglement.

E = ħω(n + 1/2)

The Observer Effect

A central paradox of quantum mechanics is the observer effect. The act of observing a quantum system inevitably changes it.

This isn't due to conscious intent; rather, any interaction – even with stray photons – disturbs the delicate superposition and forces the system to ‘choose’ a definite state.

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