/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q15CQ Consider a particle bound in a i... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Q15CQ (page 186)

Consider a particle bound in a infinite well, where the potential inside is not constant but a linearly varying function. Suppose the particle is in a fairly high energy state, so that its wave function stretches across the entire well; that is isn鈥檛 caught in the 鈥渓ow spot鈥�. Decide how ,if at all, its wavelength should vary. Then sketch a plausible wave function.

Short Answer

Expert verified

The graph is plotted with energy and potential inside a potential well.

Step by step solution

01

Location of turning points

If potential rises higher than the particles total energy then the particle is stuck in the potential well and it oscillates between the turning points and it cannot escape. Hence the turning points in this condition is located thus the oscillator wave function stretches across the entire well with quantum states with node and antinode.

02

Relation with kinetic energy and wavelength

As the kinetic energy varies inversely with wavelength, amplitude becomes larger at the regions where kinetic energy is smaller and the wavelength will be shortened for region where kinetic energy is larger

For high potential inside a well , the particles wave function tunnels through the finite potential barrier and is finally brought to zero.

03

Graph

the plausible wavefunction is

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Verify that Asin(kx) + Bcos(kx)is a solution of equation (5 - 12).

A tiny1鈥�渭g particle is in a 1 cm wide enclosure and take a yearto bounce from one end to the other and back(a) Haw many nodes are there in the enclosure (b) How would your answer change if the particle were more massive or moving faster.

In several bound systems, the quantum-mechanically allowed energies depend on a single quantum number we found in section 5.5 that the energy levels in an infinite well are given by, En=a1n2wheren=1,2,3.....andis a constant. (Actually, we known whata1is but it would only distract us here.) section 5.7 showed that for a harmonic oscillator, they areEn=a2(n鈭�12), wheren=1,2,3.....(using ann鈭�12with n strictly positive is equivalent towith n non negative.) finally, for a hydrogen atom, a bound system that we study in chapter 7,En=鈭�a3n2, wheren=1,2,3.....consider particles making downwards transition between the quantized energy levels, each transition producing a photon, for each of these three systems, is there a minimum photon wavelength? A maximum ? it might be helpful to make sketches of the relative heights of the energy levels in each case.

A comet in an extremely elliptical orbit about a star has, of course, a maximum orbit radius. By comparison, its minimum orbit radius may be nearly 0. Make plots of the potential energy and a plausible total energyversus radius on the same set of axes. Identify the classical turning points on your plot.

Write out the total wave function蠄(x,t).For an electron in the n=3 state of a 10nm wide infinite well. Other than the symbols a and t, the function should include only numerical values?
See all solutions

Recommended explanations on Physics Textbooks

Oscillations

Read Explanation

Translational Dynamics

Read Explanation

Waves Physics

Read Explanation

Fields in Physics

Read Explanation

Conservation of Energy and Momentum

Read Explanation

Magnetism and Electromagnetic Induction

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.