Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 5, Problem 82CE
To determine
The expectation value of particle’s position.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Evaluate the following expectation values: (a) ⟨ℓ,m1∣Lx∣ℓ,m2⟩ (b) ⟨ℓ,m1∣Ly∣ℓ,m2⟩
A particle is confined in a box of length L as shown in the figure. If the
potential is treated as a perturbation, including the first order
correction, the ground state energy is
(a) E =
ħ²π²
2mL²
+ V
(b) E =
ħ²π² Vo
2mL²
ħ²π² Vo
ħ²π² Vo
(c) E =
+
(d) E =
+
2mL² 4
2mL²
L/2
a) A particle is placed in the well with an energy E< Uo. Sketch the first three energy levels, and make
sure to label each one.
V(x)
U.
+2(x)
L
X
X
Chapter 5 Solutions
Modern Physics
Ch. 5 - Prob. 1CQCh. 5 - Prob. 2CQCh. 5 - Prob. 3CQCh. 5 - Prob. 4CQCh. 5 - Prob. 5CQCh. 5 - Prob. 6CQCh. 5 - Prob. 7CQCh. 5 - Prob. 8CQCh. 5 - Prob. 9CQCh. 5 - Prob. 10CQ
Ch. 5 - Prob. 11CQCh. 5 - Prob. 12CQCh. 5 - Prob. 13CQCh. 5 - Prob. 14CQCh. 5 - Prob. 15CQCh. 5 - Prob. 16CQCh. 5 - Prob. 17CQCh. 5 - Prob. 18CQCh. 5 - Prob. 19ECh. 5 - Prob. 20ECh. 5 - Prob. 21ECh. 5 - Prob. 22ECh. 5 - Prob. 23ECh. 5 - Prob. 24ECh. 5 - Prob. 25ECh. 5 - Prob. 26ECh. 5 - Prob. 27ECh. 5 - Prob. 28ECh. 5 - Prob. 29ECh. 5 - Prob. 30ECh. 5 - Prob. 31ECh. 5 - Prob. 32ECh. 5 - Prob. 33ECh. 5 - Prob. 34ECh. 5 - Prob. 35ECh. 5 - Prob. 36ECh. 5 - Prob. 37ECh. 5 - Prob. 38ECh. 5 - Prob. 39ECh. 5 - Prob. 40ECh. 5 - Prob. 41ECh. 5 - Prob. 42ECh. 5 - Obtain expression (5-23) from equation (5-22)....Ch. 5 - Prob. 44ECh. 5 - Prob. 45ECh. 5 - Prob. 46ECh. 5 - Prob. 47ECh. 5 - Prob. 48ECh. 5 - Prob. 49ECh. 5 - Prob. 50ECh. 5 - Prob. 51ECh. 5 - Prob. 52ECh. 5 - Prob. 53ECh. 5 - Prob. 54ECh. 5 - Prob. 55ECh. 5 - Prob. 56ECh. 5 - Prob. 57ECh. 5 - Prob. 58ECh. 5 - Prob. 59ECh. 5 - Prob. 60ECh. 5 - Prob. 61ECh. 5 - Prob. 62ECh. 5 - Prob. 63ECh. 5 - Prob. 64ECh. 5 - Prob. 65ECh. 5 - Prob. 66ECh. 5 - Prob. 67ECh. 5 - Prob. 68ECh. 5 - Prob. 69ECh. 5 - Prob. 70ECh. 5 - Prob. 71ECh. 5 - In a study of heat transfer, we find that for a...Ch. 5 - Prob. 73CECh. 5 - Prob. 74CECh. 5 - Prob. 75CECh. 5 - Prob. 76CECh. 5 - Prob. 77CECh. 5 - Prob. 78CECh. 5 - Prob. 79CECh. 5 - Prob. 80CECh. 5 - Prob. 81CECh. 5 - Prob. 82CECh. 5 - Prob. 83CECh. 5 - Prob. 84CECh. 5 - Prob. 85CECh. 5 - Prob. 86CECh. 5 - Prob. 87CECh. 5 - Prob. 88CECh. 5 - Consider the differential equation...Ch. 5 - Prob. 90CECh. 5 - Prob. 91CECh. 5 - Prob. 92CECh. 5 - Prob. 93CECh. 5 - Prob. 94CECh. 5 - Prob. 95CECh. 5 - Prob. 96CECh. 5 - Prob. 97CECh. 5 - Prob. 98CE
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- Physics Department PHYS4101 (Quantum Mechanics) Assignment 2 (Fall 2020) Name & ID#. A three-dimensional harmonic oscillator of mass m has the potential energy 1 1 1 V(x.y.2) = ; mw*x² +mwży² +=mw;z? where w1 = 2w a. Write its general eigenvalues and eigenfunctions b. Determine the eigenvalues and their degeneracies up to the 4th excited state c. The oscillator is initially equally likely found in the ground, first and second excited states and is also equally likely found among the states of the degenerate levels. Calculate the expectation values of the product xyz at time tarrow_forwardFor a classical system of non-interacting particles in the presence of a spherically symmetric potential V (r ) = yr, what is the mean energy per particle? y is a constant.arrow_forwardA particle with mass m is in the state mx +iat 2h V (x, t) = Ae where A and a are positive real constants. Calculate the expectation value of (p).arrow_forward
- A particle of mass m moves in a one-dimensional box of length l with the potential V = 00, Il. At a certain instant, say t 0, the wave function of this particle is %3D known to have the form V = V30/15 x (1 – x), 0 0) as a series, and expressions for the coefficients in the series.arrow_forwardConsider a particle in the one-dimensional box with the following wave function: psi(x, 0) = Cx(a−x) a. When the system is at psi(x, 0), what is ⟨x(hat)⟩? b. When the system is at psi(x, 0), what is ⟨x(hat)2⟩? c. When the system is at psi(x, 0), what is ⟨p(hat)⟩? d. When the system is at psi(x, 0), what is ⟨p(hat)2⟩? 12. When the system is at psi(x, 0), what is Δx? 13. When the system is at psi(x, 0), what is Δp?arrow_forwardB) A particle in a simultaneous eigenstates of 1² and 17. Show that the expectation value (1²) en ² 12 ≤ (12) s(1²) ≤ (l(+1)^²}/2. state satisfy th² 12 s of the particle in thisarrow_forward
- A particle in an infinite well is in the ground state with energy1.54eV. How much energy must be added to the particle to reach the second excited state (n = 3)? The third excited state (n = 4)?arrow_forwardConsider the following operators on a Hilbert space V³(C) : 0-i 0 SHABSB 101 Ly= 0 -i Lz 00 0 √2 0 i 0 LI √2 010 010 10 00 0 If the particle is in state |L₂ = −1) and L₂ is measured, what are the possible outcomes and their probabilities?arrow_forwardA particle with zero (total) energy is described by the wavefunction, Ψ(x) =A cos((n?x/L)): −L/4≤ x ≤ L/4 = 0 : elsewhere. Determine the normalization constant A. Calculate the potential energy of the particle. What is the probability that the particle will be found between x= 0 and x=L/8?arrow_forward
- (2nx sin \1.50. 2nz Consider the case of a 3-dimensional particle-in-a-box. Given: 4 = sin(ny) sin 2.00. What is the energy of the system? O 6h?/8m O 4h²/8m O 3h2/8m O none are correctarrow_forwardA particle of massm in a harmonic oscillator potential with angular frequency w is in the state (1 + {t)쭈 What is (p?) for this particle? mhw 2 O 6mħw O 3mhwarrow_forwardA particle of mass m, which moves freely inside an infinite potential well of length a, is initially in the state y(x,0)=√√3/5a sin (3xx/a)+ (1/√5a) sin (5mx/a). (a) Find y (x, t) at any later time t. Calculate the pr Lility density of thouarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning