So I tried to learn quantum mechanics in just 24 hours a while back and let's just say it did NOT go well. I used brilliant.org (yes I actually got brilliant.org) as my primary learning tool and got about three lessons through the six lesson course. So I guess here is the very little knowledge I gained from my limited foray into beginner quantum mechanics.
- In quantum mechanics, a ket is a vector (a quantity that has both magnitude and direction) that lives in some extremely complicated 'vector space' (or a realm) beyond our tangible world called Hilbert Space.
- Every quantum system can and is described by a ket.
- A ket is written with a label in between a |⟩.
- For example: | label ⟩
- When a coin is lying flat on a table it is either heads, or tails. But when it is spinning in the air it is neither until it lands.
- This is kind of how superpositions work. In quantum mechanics, superposition is the ability for quantum systems (e.g. a particle) to exist in multiple states or configurations until measured.
- This means that - mathematically and physically - an electron cam be in a state that is both |left⟩ and |right⟩ until it is measured and collapses into either one of these states.
- A superposition of two kets can be written as a sum. For example, the superposition of the kets |ket1⟩ and |ket2⟩ can be written as |ψ⟩ = a|ket1⟩ + b|ket2⟩ where a and b are numbers.
- The numbers before each ket are complex numbers (this means they can do all sorts of weird stuff like having imaginary parts!?) called amplitudes which tell us how much of the superposition is made up by each ket.
- The magnitude of one one of these amplitudes is it's absolute value. For instance, the magnitude of the amplitude a is a's absolute value and can be written as |a|. This is WAYYYYYY too complicated to explain here but the important thing to note is that the square of a ket's magnitude (e.g. |a|²) tells us the probability a system will end up in the state described by the that ket (e.g. |a⟩)
- So we can write particles (like photons) as superpositions of kets. For example: |ψ⟩ = a|0⟩ + b|1⟩. This means the particle is in a superposition of the |0⟩ and |1⟩ states until it's measured — and the values of a and b determine the probabilities of getting either result.