Question: Show that the wave function (x) = Ae ikx is a solution of Eq. 40.1 for a particle of mass m, in a region where

Show that the wave function ψ(x) = Ae ikx is a solution of Eq. 40.1 for a particle of mass m, in a region where the potential energy is a constant U0 < E. Find an expression for k, and relate it to the particle's momentum and to its de Broglie wavelength.

Step by Step Solution

★★★★★

3.49 Rating (172 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

IDENTIFY If the given wave function is a solution to the Schrdinger equation ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

P-M-P-Q-M (122).docx

120 KBs Word File

Students Have Also Explored These Related Modern Physics Questions!

Show that the wave function y = eb(xvt) is a solution of the linear wave equation (Eq. 16.27), where b is a constant.

The wave functions for a particle of mass m in a one-dimensional box of length L centered at the origin (so that the ends are at x = ?L/2) are given by Calculate and for the ground state. n= 1, 3, 5,...

Show that the function is a solution of the differential equation f(x) + f(x) = 0

Help me solve the following: A free electron has wave function V(x, t) = sin(kx - wt) (6) .Determine the electron's de Broglie wavelength, momentum, kinetic energy and speed when k = 50nm-1....

Question: 2. Consider a particle in an infinite square well. It is in the initial state y(x, 0) = A [$1(x) + $2(x)] where on (x) is the energy eigenfunctions for the infinite square well. (a) Plot...

Time-Dependent Wave Function for a Free Particle One example of a time-dependent wave function is that of a free particle [one for which U(x) = 0 for all x] of energy E and x-component of momentum p....

pls help. I'm struggling on using the solve_ivp (for a) and solve_bvp (for b and c) functions. please can you show me how to part a and b,c please? Question 12: Consider the one-dimensional,...

Particle in the box The following images shows a particle of mass m that is trapped in the second region of the potential shown that is from x=0 t x=L. In this same region the potential is zero. The...

A fellow student proposes that a possible wave function for a free particle with mass m (one for which the potential-energy function U(x) is zero) is where K is a positive constant(a) Graph this...

One- dimensional motions; Consider a particle of mass m in the onedimensional potential V(z) = mw x2/2, |x1>b; V (x) = Vo. |=| h2/mb'>> hw, i.e. a harmonic oscillator potential with a high, thin,...

As indicated in the text, both financial and nonfinancial performance indicators play important roles in an organizations overall operational control system. Explain, concisely, the relative...

You want to prepare 500.0 mL of 1.000 M KNO3 at 20C, but the lab (and water) temperature is 24C at the time of preparation. How many grams of solid KNO3 (density 2.109 g/mL) should be dissolved in a...

How many years do you have to repay a Home Buyers' Plan (HBP) withdrawal? 1 point A) 5 years B) 10 years C) 15 years D) 20 years 8. What does 'carry forward' mean for unused tuition credits? 1 point...

Reagents to accomplish the following transformation are: (a) 1. (Sia) BH; H20, HO: 2. Na Cr0, H3O" 3. NH, heat; 4. POCI, (c) (Sia) BH; H2O, HO; 2. HCN, KCN (b) (Sia) BH; H,O, HO; 2. NABH, CH,OH 3....

What is RNOA, NOPM, NOAT, NOA, NOPAT for 2017 for Harley Davidson? Consolidated Balance Sheets - USD ($) Dec. 31, 2017 $ in Thousands Current assets: Cash and cash equivalents $687,521 Marketable...

During the current year, Ron and Anne sold the following assets: (Use the dividends and capital gains tax rates and tax rate schedules.) Capital Asset L stock M stock N stock O stock Antiques Rental...

On December 31, 20x0, the Western Corporation sold inventory to Southern Inc. on the following terms: the full value of the inventory of $400,000 is payable on December 31, 20x3 and interest of 3% on...

Find the missing angle. ? 50 70

I. Fill in the blank using a number of terms listed below (@1 point). After-tax, Average, Before-tax, Bird-in-the-hand theory, Bond-yield-plus-risk-premium, Book, CAPM, Clientele effect, Common...

Solve an example of each case mentioned below: Case 01: Loan amortization table. Case 02: Choose an investment based on Payback Period, Profitability Index. Case 03: Choose an investment based on...

Question in Chemical Engineering Please Write Correct answer 7 9 .