Essential University Physics (3rd Edition)
3rd Edition
ISBN: 9780134202709
Author: Richard Wolfson
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Question
Chapter 36, Problem 66P
To determine
To show: The
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A proton has the wave function (Capital_Psi)(x) = Ae^(-x/L) with total energy equal to one-seventh its potential energy. What is the potential energy (in eV) of the particle if the wave function satisfies Schrodinger's equation? Here L = 3.80 nm.
QUESTION 9
Consider the case of a 3-dimensional particle-in-a-box. Given: Y = V8 sin(3nx) sin(2ny) sin(4rz)
What is the energy of the system?
O 24h2/8m
O sh?/8m
O none are correct
O 29h2/8m
QUESTION 10
3 πχ
sin
sin () sin
is a normalized wavefunction for the 3D particle-in-a-box.
1.5
O True
O False
A one-dimensional harmonic oscillator wave function is ψ = Axe-bx2(a) Show that ψ satisfies as shown. (b) Find b and the total energy E. (c) Is this wave function for the ground state or for the first excited state?
Chapter 36 Solutions
Essential University Physics (3rd Edition)
Ch. 36.1 - Prob. 36.1GICh. 36.2 - Prob. 36.2GICh. 36.3 - Prob. 36.3GICh. 36.4 - Prob. 36.4GICh. 36.5 - Prob. 36.5GICh. 36 - Prob. 1FTDCh. 36 - Prob. 2FTDCh. 36 - Prob. 3FTDCh. 36 - Prob. 4FTDCh. 36 - Prob. 5FTD
Ch. 36 - Prob. 6FTDCh. 36 - Prob. 7FTDCh. 36 - Prob. 8FTDCh. 36 - Prob. 9FTDCh. 36 - Prob. 10FTDCh. 36 - Prob. 11FTDCh. 36 - Prob. 12FTDCh. 36 - What distinguishes a Bose-Einstein condensate from...Ch. 36 - Prob. 14ECh. 36 - Prob. 15ECh. 36 - Prob. 16ECh. 36 - Prob. 17ECh. 36 - Prob. 18ECh. 36 - Prob. 19ECh. 36 - Prob. 20ECh. 36 - Prob. 21ECh. 36 - Prob. 22ECh. 36 - Prob. 23ECh. 36 - Prob. 24ECh. 36 - Prob. 25ECh. 36 - Prob. 26ECh. 36 - Prob. 27ECh. 36 - Prob. 28ECh. 36 - Prob. 29ECh. 36 - Prob. 30ECh. 36 - Prob. 31ECh. 36 - Prob. 32ECh. 36 - Prob. 33ECh. 36 - Prob. 34PCh. 36 - Prob. 35PCh. 36 - Prob. 36PCh. 36 - Prob. 37PCh. 36 - Prob. 38PCh. 36 - Prob. 39PCh. 36 - Prob. 40PCh. 36 - Prob. 41PCh. 36 - Prob. 42PCh. 36 - Prob. 43PCh. 36 - Prob. 44PCh. 36 - Prob. 45PCh. 36 - Prob. 46PCh. 36 - Prob. 47PCh. 36 - Prob. 48PCh. 36 - Prob. 49PCh. 36 - Prob. 50PCh. 36 - Prob. 51PCh. 36 - Prob. 52PCh. 36 - Prob. 53PCh. 36 - Prob. 54PCh. 36 - Prob. 55PCh. 36 - Prob. 56PCh. 36 - Prob. 57PCh. 36 - Prob. 58PCh. 36 - Prob. 59PCh. 36 - Prob. 60PCh. 36 - Prob. 61PCh. 36 - Prob. 62PCh. 36 - Prob. 63PCh. 36 - Prob. 64PCh. 36 - Prob. 65PCh. 36 - Prob. 66PCh. 36 - Prob. 67PCh. 36 - Prob. 68PCh. 36 - Prob. 69PCh. 36 - Prob. 70PCh. 36 - Prob. 71PCh. 36 - Prob. 72PCh. 36 - Prob. 73PCh. 36 - Prob. 74PCh. 36 - Prob. 75PCh. 36 - Prob. 76PPCh. 36 - Prob. 77PPCh. 36 - Prob. 78PPCh. 36 - Prob. 79PP
Knowledge Booster
Similar questions
- Show that normalizing the particle-in-a-box wave function ψ_n (x)=A sin(nπx/L) gives A=√(2/L).arrow_forwardA particle in a box of length L a has E1 = 2 eV. The same particle in a box of length L b has E2 = 50 eV. What is the ratio L a/L b?arrow_forwardSolving the Schrödinger equation for a particle of energy E 0 Calculate the values of the constants D, C, B, and A if knownCalculate the values of the constants D, C, B, and A if known and 2mE 2m(Vo-E) a =arrow_forward
- An electron moves with a speed v 1.25 x 10-4c inside a one-dimensional box (V = 0) of length 48.5 nm. The potential is infi nite elsewhere. The particle may not escape the box. What approximate quantum number does the electron have?arrow_forwardConsider 1D particle in a box and it’s given normalized wave function Psi = Nsin(bx) where v(x) = 0 outside the box and v(x) = cos(pix/L) inside the box from x = 0 to x = 1. (a) show that the wave function is a valid solution to the Schrödinger equation and what value of b makes it valid? (b) derive the eigenvalue expressionarrow_forwardFind the angular momentum and kinetic energy in the z axis for the Cos30eiΦ+ Sin30e-iΦ wave function.arrow_forward
- For a "particle in a box" of length, L, the wavelength for the nth level is given by An 2L %3D 2п and the wave function is n(x) = A sin (x) = A sin (x). The energy levels are пп %3D n?h? given by En : %3D 8mL2 lPn(x)|2 is the probability of finding the particle at position x in the box. Since the particle must be somewhere in the box, the integral of this function over the length of the box must be equal to 1. This is the normalization condition and ensuring that this is the case is called “normalizing" the wave function. Find the value of A the amplitude of the wave function, that normalizes it. Write the normalized wave function for the nth state of the particle in a box.arrow_forwardConsider a one-dimensional square potential well with a width of L and depth Vo. An electron is confined within this potential well. a) Calculate the energy levels of the electron in terms of L and Vo. b) Determine the wavelength of the electron associated with its lowest energy state (n=1). c) If the potential well has the width of L=5nm and Vo=10eV, calculate the energy of the electron in its lowest energy state.arrow_forwardAn electron is trapped inside a 1.00 nm potential well. Find the wavelength of the photons when the electron makes a transition from n =4 to n= 1.arrow_forward
- Equation (39.30) states that the energy of a system can have uncertainty. Does this mean that the principle of conservation of energy is no longer valid? Explain.arrow_forwardWhat is the value N so that ψ(x) = N/(a2 + x2) can give rise to a valid probability density?arrow_forwardDetermine whether Ψ(x, t) = A sin(kx - ωt) is an acceptable solution to the time-dependent Schrödinger wave equation.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Glencoe Physics: Principles and Problems, Student...PhysicsISBN:9780078807213Author:Paul W. ZitzewitzPublisher:Glencoe/McGraw-Hill
University Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax
Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Physics for Scientists and Engineers with Modern ...
Physics
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Glencoe Physics: Principles and Problems, Student...
Physics
ISBN:9780078807213
Author:Paul W. Zitzewitz
Publisher:Glencoe/McGraw-Hill
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning