Unformatted text preview: hx d dx ψ ( x )-(-i ¯ h ) d dx xψ ( x ) . (4) Now we evaluate the derivatives using the product rule: [ˆ x, ˆ p ] ψ ( x ) =-i ¯ hx dψ dx + i ¯ hψ ( x ) + i ¯ hx dψ dx = i ¯ hψ ( x ) (5) ⇒ [ˆ x, ˆ 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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- Spring '07
- Uncertainty Principle, momentum operator, Prof. Harris