Please answer these questions!! 1. (McQuarrie 3-15) Show that the average position (x) = 1/2 for all states of a 1-D particle in abox 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 particlein a box of length a. Does (p) = 0 mean that the particle is not moving? Explain.

Sure! Let's solve these quantum mechanics problems step by step: Problem 1: Average Position (z) for…

Answered: 1. (McQuarrie 3-15) Show that the…

Introductory Chemistry: A Foundation

9th Edition

ISBN:9781337399425

Author:Steven S. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Donald J. DeCoste

Chapter10: Energy

Section: Chapter Questions

Problem 3QAP

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What is the physical explanation of the difference between a particle having the 3-D rotational wavefunction 3,2 and an identical particle having the wavefunction 3,2?
Indicate which of these expressions yield an eigenvalue equation, and if so indicate the eigenvalue. a ddxcos4xb d2dx2cos4x c px(sin2x3)d x(2asin2xa) e 3(4lnx2), where 3=3f ddsincos g d2d2sincosh ddtan
In a plot of ||2, the maximum maxima in the plot is/are called the most probable positions. What is/are the most probable positions for a particle-in-a-box when: a n=1 b n=2 c n=3 d Do you see a trend?
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?
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?
A glow worm of mass 5.0 g emits red light (650nm) with a power of 0.10W entirely in the backward direction. To what speed will it have accelerated after 10y if released into free space and assumed to live? Energy emitted = P(W)-At(s). Assume the conservation of linear momentum, which means that the loss of a photon imparts an equivalent momentum in the opposite direction. total energy The total momentum imparted to the glow-worm: p = Npphoton where energy/photon x= 650nm N = Energy emitted p = mv Energyphoton V= = { PglowwormN Pphoton N = # of photons = Pphoton = momentum/photon 5g=00005kg = (mv) glowworm At =10yrs => At-see Total Energy = Pat energy/photon = (E=hr) = hec Pphoton = 12 숫
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[p* L₂ da 0 HO H + →
11. An electron in a molecule travels at a speed of 40m/s. The uncertainty in the momentum Ap of the electron is 10-6 of its momentum. Compute the uncertainty in position Ax if the mass of an electron is 9.1×10-31 kg
5
d 7-6. Evaluate the commutator: [x, -ih]. dx

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