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Latest revision as of 16:39, 7 May 2006

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

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 === major concepts ===
-* the three principles of quantum mechanics.  page 101.
+== the three principles of quantum mechanics.  page 101.==
-** with each physical system there is an associated Hilbert space.
-** at each time t, the state of the system is completely determined by a normalized vector <math>|\psi(t) \rangle</math>
+* First principle:  superposition
+** with each physical system there is an associated Hilbert space <math>{\rm E} _ {\rm H}</math>
+** at each time t, the state of the system is completely determined by a normalized vector <math>|\psi(t) \rangle</math>
+* Second principle: measurement
+** with each physical quantity <math>A \ </math> one can associate a linear hermitian operator <math>\hat{A} \ </math> mapping <math>{\rm E} _ {\rm H}</math> into  <math>{\rm E} _ {\rm H}</math>.   <math>\hat{A} \ </math> is the observable representing  <math>A \ </math>.
+** If <math>|\psi(t) \rangle</math> denotes the state of the system before a measurement, then the only possible results of a measurement are the eigenvalues <math>a_ \alpha \ </math> of  <math>\hat{A} \ </math>
+** The probability of measuring  <math>a_ \alpha \ </math> is <math>\| \psi _ \alpha \|</math>  where