More on superposition. General state of a photon and spin states  Summary and Q&A
TL;DR
Superposition is a peculiar characteristic of quantum mechanics where the combination of two states results in a new state that behaves in a nonintuitive way, with measurements having probabilities of yielding results from either of the original states.
Questions & Answers
Q: What is superposition in quantum mechanics?
Superposition refers to the combining of two quantum states to create a new state that exhibits unique properties, with measurements having probabilities of yielding results from either of the original states.
Q: How does superposition affect the measurements of quantum states?
When measuring a superposed state, the outcome can be either of the original states with different probabilities, leading to a nonintuitive behavior where the resulting state does not have properties intermediate to the original states.
Q: Why is it assumed that superimposing a state to itself does not change the physics?
Superimposing a state to itself is assumed to have no physical impact because the resulting state is physically equivalent to the original state, as long as the coefficient of the state is nonzero.
Q: How does the concept of superposition apply to photons' polarization states?
Photons' polarization states, which can be expressed with just two real parameters, can be superimposed to create the most general photon state with a complex parameter. This highlights the idea that the overall coefficient in a wave function does not impact the physics underlying the state.
Summary & Key Takeaways

Superposition is a fundamental concept in quantum mechanics where two states are combined to create a new state with unique properties.

The resulting state does not have intermediate properties between the original states.

When measuring the resulting state, the outcome can be either of the original states with different probabilities.