quantum-superposition

source: Superposition and entanglement notes

Based on the wave nature of particles, superposition is the combining of multiple waves. For example, here we see two waves with amplitudes a and b. When they combine, the superposition state has an amplitude of a + b. The relationship is linear.

Principle of quantum linear superposition = Because a physical system can be described by a wave function and Schrodinger’s wave equation, their quantum states can be linearly combined

This can be shown using the double slit experiment =

• photons are passed through a linear polarizer such that their quantum state is $|0V⟩$ where 0 shows the location, and V is for vertically polarized
• As it travels to the double slit, the state becomes a linear superposition state for $s_1$ and $s_2$ $\to |s_{1}V⟩+|s_{2}V⟩$
• quantum state vector at the screen point n $\to |({\psi }_n+{\Phi }_n)nV⟩$ where
  • ${\psi }_n\text{ and }{\Phi }_n$ are the probability amplitude coefficients for starting from $s_1$ and $s_2$ respectively