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# 348-problem27 - Calculate p and 2 p for this system by...

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Chem. 540 Instructor: Nancy Makri PROBLEM 27 The uncertainty x in the position of a particle is given by the root mean square deviation of the particle from its mean position; i.e., ( 29 1 2 2 2 x x x ∆ = - . Similarly, the uncertainty p in the momentum of a particle is given by the root mean square devi- ation of the particle from its mean momentum: ( 29 1 2 2 2 p p p ∆ = - Consider again a particle in a one-dimensional square well of length L . a) Calculate x and 2 x for this system. Use your results to find the uncertainty x in posi- tion. b)
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Unformatted text preview: Calculate p and 2 p for this system by using the form of the momentum operator in posi-tion space. Notice that there is another way to obtain 2 p in this case, using the relation between the square of the momentum and the total energy (which is known for every value of n ). Use this observation to check your result. c) Use your results to find the uncertainty p ∆ in momentum and show that / 2 x p ∆ ∆ ≥ h for all values of n , consistent with the uncertainty principle....
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