Lecture #13: Schrodinger Equation Flashcards
Three components of theory
State, evolution, results
Quantum state
Ket in Hilbert space
Quantum evolution
Schrodinger equation
Quantum results
Projection postulate: only certain quantized results are possible
- the state collapses into one of the eigenstates
Old quantum theory
The system obeys classical mechanical rules, but not every motion allowed, only those obeying the quantization condition
Properties of waves
linearity, superposition, interference, propagation
Waves are solutions to certain PDE’s that are proportional to their
Second derivatives
F= ma tells you the acceleration, but what is the state?
(x,v)
At one of the verticals of a vibrating string, the net force is
Zero
At the curvature of a vibrating string, the net force is
Downwards
The Hamiltonian H represents the
Total energy of the system
the action of calculating d/dx(some wave) means that d/dx acts like an
Operator
The Hamiltonian operates on some state and you get back the energy. What is the state referred to as?
Energy eigenstate
The laws of physics are always differential equations because
Given knowledge of state(t), they tell you d/dtstate(t)
