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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.

The uncertainty principle is an inequality that is satisfied by the product of the uncertainties of two Hermitian operators that fail to commute. Since the uncertainty of an operator on any given physical state is a number greater than or equal to zero, the …

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