postulates-handout - Chem. 540 Instructor: Nancy Makri...

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Unformatted text preview: Chem. 540 Instructor: Nancy Makri Postulates of Quantum Mechanics 1. Wavefunction The state of a system is described by a vector in a Hilbert space. The state of a system can be fully specified by its wavefunction in position space, ( ; ) t r , or by its wavefunction in momentum space, ( ; ) t p % etc. The probability of finding the particle within a volume d r around point r is equal to 2 ( ) d r r . In order for the probability of finding the particle anywhere to be equal to unity, we require wavefunctions to be normalized: 2 ( ) 1 d = r r . Hilbert space: A vector space (over complex-valued vectors) of up to infinite dimension, which is complete, and in which the inner product * u v is finite. 2. Operators States are transformed by linear operators: 1 2 1 2 ( ) A A A + = + . The commutator of two operators , A B is defined as [ , ] A B AB BA - ....
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This note was uploaded on 02/08/2012 for the course CHEM 540 taught by Professor Mccall during the Fall '08 term at University of Illinois, Urbana Champaign.

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postulates-handout - Chem. 540 Instructor: Nancy Makri...

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