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--- topic:qm:postulates [2022/12/09 19:11] – samuel
+++ topic:qm:postulates [2023/02/15 18:26] (current) – samuel
@@ Line 8: / Line 8: @@
 The system is completely described by its state vector, which is a unit vector in the system’s state space.
-**2.** The evolution of a closed quantum system is described by a unitary transformation.
+**2.** The evolution of a closed quantum system is described by a [[topic:math:linalg:operator|unitary]] transformation.
 That is, the state $\ket{\psi}$ of the system at time t1 is related to the state $\ket{\psi'}$ of the system at time t2 by a unitary operator U which depends only on the times t1 and t2, $\ket{\psi'} = U \ket{\psi}$
@@ Line 19: / Line 19: @@
 H is a fixed Hermitian operator known as the //Hamiltonian// of the closed system.
-**3.** Quantum measurements are described by a collection ${M_m}$ of measurement operators.
+**3.** [[topic:qm:measurements|Quantum measurements]] are described by a collection ${M_m}$ of measurement operators.
 These are operators acting on the state space of the system being measured.
-The index m refers to the measurement outcomes that may occur in the experiment.
+The index $m$ refers to the measurement outcomes that may occur in the experiment.
 If the state of the quantum system is $\ket{\psi}$ immediately before the measurement then the probability that result $m$ occurs is given by
 $$p(m) = \Braket{\psi | M_m^\dag M_m | \psi}$$

Kollektanee - Samuel Gyger