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the three principles of quantum mechanics. page 101.

• First principle: superposition
  • with each physical system there is an associated Hilbert space E_H
  • at each time t, the state of the system is completely determined by a normalized vector $|\psi(t) \rangle$

• Second principle: measurement
  • with each physical quantity $A \$ one can associate a linear hermitian operator $\hat{A} \$ mapping E_H into E_H. $\hat{A} \$ is the observable representing $A \$.
  • If $|\psi(t) \rangle$ denotes the state of the system before a measurement, then the only possible results of a measurement are the eigenvalues $a_ \alpha \$ of $\hat{A} \$
  • The probability of measuring $a_ \alpha \$ is $\| \psi _ \alpha \|$ where