Transcription of Quantum Physics II, Lecture Notes 5 - MIT OpenCourseWare
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Quantum Physics II, Lecture Notes 5 - MIT OpenCourseWare
UNCERTAINTY PRINCIPLE AND COMPATIBLE OBSERVABLES B. Zwiebach October 21, 2013 Contents 1 Uncertainty defined 1 2 The Uncertainty Principle 3 3 The Energy-Time uncertainty 6 4 Lower bounds for ground state energies 9 5 Diagonalization of Operators 11 6 The Spectral Theorem 12 7 Simultaneous Diagonalization of Hermitian Operators 16 8 Complete Set of Commuting Observables 18 1 Uncertainty defined As we know, observables are associated to Hermitian operators. Given one such operator A we can use it to measure some property of the physical system, as represented by a state.
Even without quantum mechanical considerations we can ask the observer what was the angular frequency ω of the pulse. In order to answer our question the observer will attempt to count the number N of complete oscillations of the waveform that went through. Of course, this number N is
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