Lecture 5 - Quantum Superposition

What we think of as "state" such as the electron in hydrogen being in energy level $n=1$ or $n=2$ are actually the eigenstates of the electron in the hydrogen atom. These are the wavefunctions that came out of the Schrodinger equation for different values of $n,l,m$.

Mathematically, any sum of these wave functions also solves the Schrodinger equation, which means that the electron can be in both $n=1$ or $n=2$.

Such a sum of two or more wave function is called a quantum superposition.

What does this mean?

That means that we can have two different states occuring at the same time. See Reading 3 - Electron Configs, Braket Notation, Hilbert Spaces and Sch. Eqtn.#3.4.1 Schrodinger's Cate Thought Experiment.

Really the key to making sure that the wave function doesn't collapse is to have nothing observe it, or give hint of observing it.