/*! 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} Q45P 聽Consider a beam of free partic... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Q45P (page 1356)

Consider a beam of free particles that move with velocityv=p/min thex-direction and are incident on a potential energy stepU(x) = 0, forx <0, andU(x) =U0<E, forx> 0. The wave function forx< 0 is蠄(x)=Aeik1x+Be-ik1x, representing incident and reflected particles, and forx> 0 is蠄(x)=Ceik2x, representing transmitted particles. Use the conditions that both蠄and its first derivative must be continuous at x = 0 to find the constants B and C in terms of k1, k2, and A.

Short Answer

Expert verified

a) The value of constants is B=k1-k2k1+k2Aand role="math" localid="1664007828935" C=2k2k1+k2A

Step by step solution

01

(a) Identification of the concept

The wave function of region x < 0 denoted as region 1 is,

蠄1=Aei鈥�k1x+Be-鈥�i鈥�k1x, .......(A)

The wave function of region x > 0 denoted as region 2 is,

蠄1=Ceik2x ......(B)

According to the question, the conditions to be used are,

(i)鈥�蠄1(0)=蠄2(0)

(ii)鈥�at鈥�x=0,鈥�诲蠄1dx=诲蠄2dx鈥�

02

(b) Determination of the values of constants B and C in terms of k1, k2, and A.

From equation (i), Put teh wave function defined in equation (A) and (B) to obtain,

A+B=C

Similarly, from equation (ii), Put teh wave function defined in equation (A) and (B) to obtain,

ik1A-ik1B=ik2C

The two pairs of equations can be solved and the result in terms of k1, k2 and A is,

B=k1-k2k1+k2A

And,

C=2k2k1+k2A

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

Analysis of the photon absorption spectrum of a diatomic molecule shows that the vibrational energy levels for small values of n are very nearly equally spaced but the levels for large n are not equally spaced. Discuss the reason for this observation. Do you expect the adjacent levels to move closer together or farther apart as n increases? Explain.

During the photoelectric effect, light knocks electrons outof metals. So why don鈥檛 the metals in your home lose their electrons when you turn on the lights?

In an experiment involving the photoelectric effect, if the intensity of the incident light (having frequency higher than the threshold frequency) is reduced by a factor of 10 without changing anything else, which (if any) of the following statements about this process will be true? (a) The number of photoelectrons will most likely be reduced by a factor of 10. (b) The maximum kinetic energy of the ejected photoelectrons will most likely be reduced by a factor of 10. (c) The maximum speed of the ejected photoelectrons will most likely be reduced by a factor of 10. (d) The maximum speed of the ejected photoelectrons will most likely be reduced by a factor of 110. (e) The time for the first photoelectron to be ejected will be increased by a factor of 10.

Speeds of molecules in a gas vary with temperature, whereas speeds of electrons in the conduction band of a metal are nearly independent of temperature. Why are these behaviors so different?

Since lead is a stable element, why doesn鈥檛 the U238decay series shown in Fig. 43.7 stop at lead, P214b?
See all solutions

Recommended explanations on Physics Textbooks

Wave Optics

Read Explanation

Astrophysics

Read Explanation

Waves Physics

Read Explanation

Dynamics

Read Explanation

Oscillations

Read Explanation

Particle Model of Matter

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.