Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
expand_more
expand_more
format_list_bulleted
Question
Chapter 5, Problem 83CE
To determine
Uncertainty in the position of particle
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A 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 3mhw
Harmonic 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
2
Problem 3. Consider the two example systems from quantum mechanics. First, for a
particle in a box of length 1 we have the equation
h² d²v
EV,
2m dx²
with boundary conditions (0) = 0 and V(1) = 0.
Second, the Quantum Harmonic Oscillator (QHO)
=
h² d²
+kr²V = EV
2m dg²+ka²
1/ k2²) v
(a) Write down the states for both systems. What are their similarities and differences?
(b) Write down the energy eigenvalues for both systems. What are their similarities
and differences?
(c) Plot the first three states of the QHO along with the potential for the system.
(d) Explain why you can observe a particle outside of the "classically allowed region".
Hint: you can use any state and compute an integral to determine a probability of
a particle being in a given region.
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
Similar questions
- Consider an anisotropic 3D harmonic oscillator where we = Wy the energy of the particle in the following state (nx, ny, n₂) = (0, 0, 2)? = w and wz A. 4ħw B. 6hw C. 3ħw D. 2.5ħw = 2w. What isarrow_forwardAn electron moving in a box of length ‘a’. If Z1 is the wave function at x1 = a/4 with n=1 and Z2 at x = a/4 for n=2 find Z1/Z2arrow_forwardA 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/2arrow_forward
- An electron (m = 9.109*10^-31 kg) is confined in a one-dimensional infinite square well of width L = 10 nm. determine energy for first excited energy statearrow_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_forwardAn electron confined to a one-dimensional box of length is in its third energy state. What is the probability of finding the electron in the region x = 0 to x = {/4?|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_forwardThe normalized solution to the Schrodinger equation for a particular potential is ψ = 0 for x <0, and Ψ(x)=(2/a^{3/2}) x exp(-ax) for x>=0. What is the probability of finding a particle at this potential between x = a - 0.027a and x = a + 0.027a?arrow_forwardA 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_forward
- 8-6. If you were to use a trial function of the form p(x) = (1+cax²)e-ax²/2, where a = (ku/h²)1/2 and c is a variational parameter, to calculate the ground-state energy of a harmonic oscillator, what do you think the value of c will come out to be? Why?arrow_forwardA 1-D harmonic oscillator is in the state e(x) = 1//14 [34o(x) - 241(x) + µ2(x)] are the ground, first excited and second excited states, respectively. The probability of finding the oscillator in the ground state is 1 9/14 3//14arrow_forwardA particle with mass m is in the state тс V (x,t) = Ae +iat 2h where A and a are positive real constants. Calculate the potential energy function that satisfies the Schrodinger equation.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning
University Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax
Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
Physics for Scientists and Engineers with Modern ...
Physics
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning