Introduction to Quantum Mechanics
Quantum Mechanics: A framework of physics
Quantum Physics: Application of QM on physics, E.g. String Theory (QM + gravity)
Topics:
1. Linearity of QM
2. Complex Number
3. Loss of Determinism
4. Superposition
5. Entanglement
Prep: A theory
Theory of Motion = Equations of Motion (EOM) + Dynamical Variables
I. Linearity
𝐿𝑢 = 0
𝐿(𝑢, 𝑣, 𝑚 … ) = 0
L is the linearity Operator, u is the unknown
𝐿(𝑎𝑢) = 𝑎𝐿(𝑢)
𝐿(𝑢) + 𝐿(𝑤) = 𝐿(𝑢 + 𝑤)
𝐿(𝑎𝑢 + 𝑏𝑤) = 𝑎𝐿(𝑢) + 𝑏𝐿(𝑤)
If 𝐿(𝑢) = 𝐿(𝑤) = 0 ,
𝐴𝑢 + 𝑏𝑤 is a solution
For a linear function, e.g. Maxwell Equations:
1. F(x) is a solution, F(ax) is a solution
2. F(x1) and F(x2) are solutions, F (x1 + x2) is a solution.
3. All solutions are superpositional.
E.G.
𝑑𝑢 1
+ 𝑢
𝑑𝑡 𝜏
Is a linear equation
L(u) =