References

# Quantum Mechanics

## 1. Superposition

Quantum state is a (complex) superposition of classical states.

Here, the coefficients are complex numbers called amplitudes.

The states

are the basis of the N-dimensional Hilbert space.

For example, the state can be spin state, angular momentum, etc.

## 2. Measurement

The (superposed) state is not observable, but the we will see only one of the classical state by "measurement". The probability of measurement to a state, |j>, is the square of the amplitude.

$$P(j) = |\alpha_j|^2$$

The measurement is non-unitary, i.e., irreversible.

## 3. Unitary Evolution

Operator: change a state to another state