Physics for Scientists and Engineers, Vol. 1
6th Edition
ISBN: 9781429201322
Author: Paul A. Tipler, Gene Mosca
Publisher: Macmillan Higher Education
expand_more
expand_more
format_list_bulleted
Question
Chapter 35, Problem 6P
To determine
The proofthat expectation value for ground state and first excited state is zero.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Evaluate <x>, <px>, △x, △px, and △x△px for the provided normalized wave function.
Consider a particle in a box of length L= 1 for the n= 2 state. The wave function is defined as:
(x) =
sin (27x)
%3|
Normalize the wave function.
Step by step and integrate the wavefunction from 0 to 2pi
Chapter 35 Solutions
Physics for Scientists and Engineers, Vol. 1
Ch. 35 - Prob. 1PCh. 35 - Prob. 2PCh. 35 - Prob. 3PCh. 35 - Prob. 4PCh. 35 - Prob. 5PCh. 35 - Prob. 6PCh. 35 - Prob. 7PCh. 35 - Prob. 8PCh. 35 - Prob. 9PCh. 35 - Prob. 10P
Ch. 35 - Prob. 11PCh. 35 - Prob. 12PCh. 35 - Prob. 13PCh. 35 - Prob. 14PCh. 35 - Prob. 15PCh. 35 - Prob. 16PCh. 35 - Prob. 17PCh. 35 - Prob. 18PCh. 35 - Prob. 19PCh. 35 - Prob. 20PCh. 35 - Prob. 21PCh. 35 - Prob. 22PCh. 35 - Prob. 23PCh. 35 - Prob. 24PCh. 35 - Prob. 25PCh. 35 - Prob. 26PCh. 35 - Prob. 27PCh. 35 - Prob. 28PCh. 35 - Prob. 29PCh. 35 - Prob. 30PCh. 35 - Prob. 31PCh. 35 - Prob. 32PCh. 35 - Prob. 33PCh. 35 - Prob. 34PCh. 35 - Prob. 35PCh. 35 - Prob. 36PCh. 35 - Prob. 37PCh. 35 - Prob. 38P
Knowledge Booster
Similar questions
- A particle of mass m is trapped in a three-dimensional rectangular potential well with sides of length L, L/ √2, and 2L. Inside the box V = 0, outside V = ∞. Assume that Ψ = Asin (k1x) sin (k2y) sin (k3z) inside the well. Substitute this wave function into the Schrödinger equation and apply appropriate boundary conditions to find the allowed energy levels. Find the energy of the ground state and first four excited levels. Which of these levels are degenerate?arrow_forwardprovided that a particle is described by the normalized wavefunction ψ(x)=(2a/π)1/4e-ax^2 with a=constant and -∞ ≤ x ≤ ∞. Calculate the expectation values (⟨x⟩,⟨x2⟩, ⟨px⟩, ⟨p2x⟩, then calculate Δpx= {⟨p2x⟩-⟨px⟩2}1/2 and Δx= {⟨x2⟩-⟨x⟩2}1/2. Finally, verify that the value of ΔpxΔx is consistent with Heisenberg's uncertainty principle. Show full and complete procedure in a clear way. DO NOT SKIP ANY STEParrow_forwardLet ₁ (x) and ₂ (x) be normalized stationary states (energy eigenfunctions) of an one- dimensional system for unequal energies E₁ and E2. Let Y (x; t) be the wave function of the system, and suppose that at t = 0 it is given by Y (x; t = 0) = A[ ¥₁ (x) + (1 - i) 4₂ (x)] a) Determine A such that Y (x; t = 0) is normalized. b) Write down the wave function Y (x; t) at time t. Is Y (x; t) a stationary state? Explain. c) Does the probability density |Y (x; t)|² vary with time?arrow_forward
- Is the function Ψ = xe−x^2/2 an eigenfunction of the operator Aˆ = −∂2/∂x2+ x2 ?arrow_forwardA particle of mass m is confined to a one-dimensional (1D) infinite well (i.e., a 1D box) of width 6 m. The potential energy is given by (0 6m) The particle is in the n=5 quantum state. What is the lowest positive value of x (in m) such that the particle has zero probability of being found at x?arrow_forwardA particle of mass m is confined to a harmonic oscillator potential V(x) = (1/2)kx². The particle starts off at t = 0 in the state yo + W1 where yn are the normalized energy eigenstates of the oscillator. (a) Sketch (axes, labels, no numbers needed) the wave function at t = 0. (b) Write an expression for y(x,t) for all t 2 0. . (c) Calculate the expectation value of the particle's position and momentum at all times t2 0. !arrow_forward
- A wave function of a particle with mass m is given by, Acosaz -Ist, where a = 1.00 × 100/m. (z) ={0 otherwise Find the normalization constant A.arrow_forwardHarmonic oscillator eigenstates have the general form 1 μω ,1/4 μω AG)(√(-) n ħ In this formula, which part determines the number of nodes in the harmonic oscillator state? = y (x) 1 √(™ ћn 2"n! Holev 1/4 μω 1 2"n! exp(-1022²) 2ħ μω ħ 2"n! exp μω χ 2ħ 2arrow_forwardA particle is described by the wave function [V5 cos 0 + sin(e + 4) + sin(0 – ø)], 2/3n (a) Express 4(0, 4) in terms of spherical harmonics (b) Calculate p and Lzµ. Is y an eigenstate of I? and L,? (c) Calculate Î44 and (L4) If the measurement of Î, is carried out, find the probability of getting the results 0,ħ and -ħ. (d)arrow_forward
- U = U, %3D U = 0 X = 0 A potential step U(x) is defined by U(x) = 0 for x 0 If an electron beam of energy E > U, is approaching from the left, write the form of the wave function in region I (x 0) in terms of the electron mass m, energy E, and potential energy U,. Do not bother to determine the constant coefficients. Formulas.pdf (Click here-->) Edit Vicw Insert Format Tools Table 12pt v Paragraph BIU Av eu T? varrow_forwardWith clear stepsarrow_forwardNormalize the wave function 4(x) = [Nr2(L−x) 0arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
Recommended textbooks for you
College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
University Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSON
Introduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Lecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
University Physics (14th Edition)
Physics
ISBN:9780133969290
Author:Hugh D. Young, Roger A. Freedman
Publisher:PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:9781107189638
Author:Griffiths, David J., Schroeter, Darrell F.
Publisher:Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:9780321820464
Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...
Physics
ISBN:9780134609034
Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:PEARSON