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Unformatted text preview: hx d dx ( x )-(-i h ) d dx x ( x ) . (4) Now we evaluate the derivatives using the product rule: [ x, p ] ( x ) =-i hx d dx + i h ( x ) + i hx d dx = i h ( x ) (5) [ x, p ] = i h. (6) By substitution we have shown that the momentum operator for a 1D system as deFned in class obeys the commutation relation and therefore obeys the uncertainty principle for position and momentum. This shows that the momentum operator in Equation 1 is acceptable. 1...
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This note was uploaded on 01/25/2011 for the course CHEM 120A taught by Professor Whaley during the Spring '07 term at University of California, Berkeley.
- Spring '07