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The uncertainty principle is related to the order of the two operators operating on a wavefunction. Evaluate the expressions
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Chapter 10 Solutions
EBK PHYSICAL CHEMISTRY
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- Consider a 1D particle in a box confined between a = 0 and x = 3. The Hamiltonian for the particle inside the box is simply given by Ĥ . Consider the following normalized wavefunction 2m dz² ¥(2) = 35 (x³ – 9x). Find the expectation value for the energy of the particle inside the box. Give your 5832 final answer for the expectation value in units of (NOTE: h, not hbar!). In your work, compare the expectation value to the lowest energy state of the 1D particle in a box and comment on how the expectation value you calculated for the wavefunction ¥(x) is an example of the variational principle.arrow_forwardConsider a fictitious one-dimensional system with one electron.The wave function for the electron, drawn below, isψ (x)= sin x from x = 0 to x = 2π. (a) Sketch the probabilitydensity, ψ2(x), from x = 0 to x = 2π. (b) At what value orvalues of x will there be the greatest probability of finding theelectron? (c) What is the probability that the electron willbe found at x = π? What is such a point in a wave functioncalled?arrow_forwardThe normalized wave function for a particle in a one- dimensional box in which the potential energy is zero is (x) = /2/L sin (nTx/L), where L is the length of the box (with the left wall at x = 0). What is the probability that the particle will lie between x = 0 and x = ticle is in its n = 2 state? L/4 if the par-arrow_forward
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