1. (McQuarrie 3-15) Show that the average position (x) = 1/2 for all states of a 1-D particle in a box of length a. Is this result physically reasonable? 2. (McQuarrie 3-16) Show that the average momentum (p) = 0 for all states of a 1-D particle in a box of length a. Does (p) = 0 mean that the particle is not moving? Explain.

1. (McQuarrie 3-15) Show that the average position (x) = 1/2 for all states of a 1-D particle in a box of length a. Is this result physically reasonable? 2. (McQuarrie 3-16) Show that the average momentum (p) = 0 for all states of a 1-D particle in a box of length a. Does (p) = 0 mean that the particle is not moving? Explain.

Physical Chemistry

2nd Edition

ISBN:9781133958437

Author:Ball, David W. (david Warren), BAER, Tomas

Publisher:Ball, David W. (david Warren), BAER, Tomas

Chapter10: Introduction To Quantum Mechanics

Section: Chapter Questions

Problem 10.61E: In a plot of ||2, the maximum maxima in the plot is/are called the most probable positions. What...

See similar textbooks

Similar questions

For a particle in a state having the wavefunction =2asinxa in the range x=0toa, what is the probability that the particle exists in the following intervals? a x=0to0.02ab x=0.24ato0.26a c x=0.49ato0.51ad x=0.74ato0.76a e x=0.98ato1.00a Plot the probabilities versus x. What does your plot illustrate about the probability?
(a) For a particle in the stationary state n of a one dimensional box of length a, find the probability that the particle is in the region 0xa/4.(b) Calculate this probability for n=1,2, and 3.
For a particle in the stationary state n of a one dimensional box of length a, find the probability that the particle is in the region 0 xa/4. (b) Calculate this probability for n = 1, 2, and 3
Which of these choices is the expectation value of momentum p for a particle in the state n = 5 in a square well potential. hL/4 h/4L^2 0 hL/2 h/L^2
For a 1.0 x 10^-26 g particle in a box whose ends are at x=0 and x=2.000 Å, calculate the probability that the x coordinate is between 1.6000 and 1.6001 Å
A glow-worm of mass 5.0 g emits red light (650 nm) with a power of 0.10 W entirely in the backward direction. To what speed will it have accelerated after 10 y if released into free space and assumed to live?
Calculate the linear momentum of a pickup truck that has a mass of 945 kg and is traveling eastward at 26 m/s.
For a particle in a two-dimensional box with sides of equal lengths, draw rough sketches of contours of constant || for the states (a) nx=2, ny=1; (b) nx =2, ny=2. At what points in the box is || a maximum for each state?
For a system consisting of three particles in 3D, on what variables does the time-independent wave function c depend?
For this I got 1.1, I just wanted to make sure that it was correct
Consider a particle of mass m confined to a one-dimensional box of length L and in a state with normalized wavefunction ψn. (a) Without evaluating any integrals, explain why ⟨x⟩ = L/2. (b) Without evaluating any integrals, explain why ⟨px⟩ = 0. (c) Derive an expression for ⟨x2⟩ (the necessary integrals will be found in the Resource section). (d) For a particle in a box the energy is given by En = n2h2/8mL2 and, because the potential energy is zero, all of this energy is kinetic. Use this observation and, without evaluating any integrals, explain why <p2x> = n2h2/4L2.
Calculate the linear momentum of a pickup truck that has a mass of 915 kg and is traveling eastward at 22 m/s. kg · m/s