![Fundamentals of Physics, Volume 1, Chapter 1-20](https://www.bartleby.com/isbn_cover_images/9781118233764/9781118233764_largeCoverImage.gif)
Fundamentals of Physics, Volume 1, Chapter 1-20
10th Edition
ISBN: 9781118233764
Author: David Halliday
Publisher: WILEY
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 38, Problem 61P
To determine
To show:
Eq.38-27 is a solution of Schrödinger’s equation, with
Expert Solution & Answer
![Check Mark](/static/check-mark.png)
Want to see the full answer?
Check out a sample textbook solution![Blurred answer](/static/blurred-answer.jpg)
Students have asked these similar questions
*24 Figure 39-30 shows a two-dimen-
sional, infinite-potential well lying in an
xy plane that contains an electron. We
probe for the electron along a line that
bisects L, and find three points at which
the detection probability is maximum. Figure 39-30 Problem 24.
Those points are separated by 2.00 nm.
Then we probe along a line that bisects L, and find five points at
which the detection probability is maximum. Those points are sep-
arated by 3.00 nm. What is the energy of the electron?
Find the angular momentum and kinetic energy in the z axis for the
(cos(30))*e(iΦ)+(sin(30))*e(-iΦ) wave function.
22 A particle is confined to the one-dimensional infinite poten-
tial well of Fig. 39-2. If the particle is in its ground state, what
is its probability of detection between (a) x = 0 and x = 0.30L.
(b) x = 0.70L and x = L, and (c) x = 0.30L and x = 0.70L?
U(x)
Fig 39-2
Chapter 38 Solutions
Fundamentals of Physics, Volume 1, Chapter 1-20
Ch. 38 - Prob. 1QCh. 38 - Prob. 2QCh. 38 - Prob. 3QCh. 38 - Prob. 4QCh. 38 - Prob. 5QCh. 38 - Prob. 6QCh. 38 - Prob. 7QCh. 38 - Prob. 8QCh. 38 - Prob. 9QCh. 38 - Prob. 10Q
Ch. 38 - Prob. 11QCh. 38 - Prob. 12QCh. 38 - Prob. 13QCh. 38 - Prob. 14QCh. 38 - Prob. 15QCh. 38 - Prob. 16QCh. 38 - Prob. 1PCh. 38 - Prob. 2PCh. 38 - Prob. 3PCh. 38 - Prob. 4PCh. 38 - Prob. 5PCh. 38 - Prob. 6PCh. 38 - Prob. 7PCh. 38 - Prob. 8PCh. 38 - Prob. 9PCh. 38 - Prob. 10PCh. 38 - Prob. 11PCh. 38 - Prob. 12PCh. 38 - Prob. 13PCh. 38 - Prob. 14PCh. 38 - Prob. 15PCh. 38 - Prob. 16PCh. 38 - Prob. 17PCh. 38 - Prob. 18PCh. 38 - Prob. 19PCh. 38 - Prob. 20PCh. 38 - Prob. 21PCh. 38 - Prob. 22PCh. 38 - Prob. 23PCh. 38 - Prob. 24PCh. 38 - Prob. 25PCh. 38 - Prob. 26PCh. 38 - Prob. 27PCh. 38 - Prob. 28PCh. 38 - Prob. 29PCh. 38 - Prob. 30PCh. 38 - Prob. 31PCh. 38 - Prob. 32PCh. 38 - Prob. 33PCh. 38 - Prob. 34PCh. 38 - Prob. 35PCh. 38 - Prob. 36PCh. 38 - Prob. 37PCh. 38 - Prob. 38PCh. 38 - Prob. 39PCh. 38 - Prob. 40PCh. 38 - Prob. 41PCh. 38 - Prob. 42PCh. 38 - Prob. 43PCh. 38 - Prob. 44PCh. 38 - Prob. 45PCh. 38 - Prob. 46PCh. 38 - Prob. 47PCh. 38 - Prob. 48PCh. 38 - Prob. 49PCh. 38 - Prob. 50PCh. 38 - Prob. 51PCh. 38 - Prob. 52PCh. 38 - Prob. 53PCh. 38 - Prob. 54PCh. 38 - Prob. 55PCh. 38 - Prob. 56PCh. 38 - Prob. 57PCh. 38 - Prob. 58PCh. 38 - Prob. 59PCh. 38 - Prob. 60PCh. 38 - Prob. 61PCh. 38 - Prob. 62PCh. 38 - Prob. 63PCh. 38 - Prob. 64PCh. 38 - Prob. 65PCh. 38 - Prob. 66PCh. 38 - Prob. 67PCh. 38 - Prob. 68PCh. 38 - Prob. 69PCh. 38 - Prob. 70PCh. 38 - Prob. 71PCh. 38 - Prob. 72PCh. 38 - Prob. 73PCh. 38 - Prob. 74PCh. 38 - Prob. 75PCh. 38 - Prob. 76PCh. 38 - Prob. 77PCh. 38 - Prob. 78PCh. 38 - Prob. 79PCh. 38 - Prob. 80PCh. 38 - Prob. 81PCh. 38 - Prob. 82PCh. 38 - Prob. 83PCh. 38 - Prob. 84PCh. 38 - Prob. 85PCh. 38 - Prob. 86PCh. 38 - Prob. 87PCh. 38 - Prob. 88PCh. 38 - Prob. 89PCh. 38 - Prob. 90P
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
- 16 For three experiments, Fig. 38-25 gives the transmission coefficient T for electron tunneling through a po- tential barrier, plotted versus barrier thickness L. The de Broglie wave- lengths of the electrons are identical in the three experiments. The only difference in the physical setups is the barrier heights U. Rank the three experiments according to U, greatest first. T: Figure 38-25 Question 16.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_forwardShow that the following function Y(0,9)= sin 0 cos e eiº is the solution of Schrödinger 1 1 equation: sin 0 21 sin 0 00 Y(0,0)= EY (0,9) and find the sin 0 dp? energy, E.arrow_forward
- An electron with initial kinetic energy 5.0 eV encounters a barrier with height U0 and width 0.60 nm. What is the transmission coefficient if (a) U0 = 7.0 eV; (b) U0 = 9.0 eV; (c) U0 = 13.0 eV?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 thin solid barrier in the xy-plane has a 12.6µm diameter circular hole. An electron traveling in the z-direction with vx 0.00m/s passes through the hole. Afterward, within what range is vx likely to be?arrow_forward
- A student in a physics laboratory observes a hydrogen spectrum with a diffraction grating for the purpose of measuring the wavelengths of the emitted radiation, hr the spectrum, she observes a yellow line and finds its wavelength to be 589 nm. (a) Assuming that this is part of the Balmer series, determine the principal quantum number of the initial state, (b) What is unreasonable about this result? (c) Which assumptions are unreasonable 01 inconsistent?arrow_forwardFor a particle in one dimension in a region of constant potential energy Vo, the angular frequency w and the wave number k of its associated wave function are related by h²k? ħw = + Vo 2m а) - Verify that, if a monochromatic wave of the form ý = ei(kz-wt) is substituted into the Schrödinger time dependent equation, the above relation is reproduced. b) - c) In which region(s) of space are you most likely to find this particle? Why do we demand that the wavefunction be identically zero outside of the "box" in the particle in a box model?arrow_forwardA particle with mass m is moving in three-dimensions under the potential energy U(r), where r is the radial distance from the origin. The state of the particle is given by the time-independent wavefunction, Y(r) = Ce-kr. Because it is in three dimensions, it is the solution of the following time-independent Schrodinger equation dıp r2 + U(r)µ(r). dr h2 d EÞ(r) = 2mr2 dr In addition, 00 1 = | 4ar?y? (r)dr, (A(r)) = | 4r²p²(r)A(r)dr. a. Using the fact that the particle has to be somewhere in space, determine C. Express your answer in terms of k. b. Remembering that E is a constant, and the fact that p(r) must satisfy the time-independent wave equation, what is the energy E of the particle and the potential energy U(r). (As usual, E and U(r) will be determined up to a constant.) Express your answer in terms of m, k, and ħ.arrow_forward
- In your research on new solid-state devices, you are studying a solid-state structure that can be modeled accurately as an electron in a one-dimensional infinite potential well (box) of width L. In one of your experiments, electromagnetic radiation is absorbed in transitions in which the initial state is the n = 1 ground state. You measure that light of frequency f = 9.0x 1014 Hz is absorbed and that the next higher absorbed frequency is 16.9 x 1014 Hz. (a) What is quantum number n for the final state in each of the transitions that leads to the absorption of photons of these frequencies? (b) What is the width L of the potential well? (c) What is the longest wavelength in air of light that can be absorbed by an electron if it is initially in the n = 1 state?arrow_forwardE 0 V 0 Q/Solve the Schrödinger equation for regions x0 to calculate the reflection coefficient, R. Where Earrow_forwardarrow_back_iosarrow_forward_ios
Recommended textbooks for you
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningUniversity Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
![Text book image](https://www.bartleby.com/isbn_cover_images/9781133104261/9781133104261_smallCoverImage.gif)
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
![Text book image](https://www.bartleby.com/isbn_cover_images/9781337553292/9781337553292_smallCoverImage.gif)
Physics for Scientists and Engineers with Modern ...
Physics
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
![Text book image](https://www.bartleby.com/isbn_cover_images/9781938168185/9781938168185_smallCoverImage.gif)
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax
![Text book image](https://www.bartleby.com/isbn_cover_images/9781133939146/9781133939146_smallCoverImage.gif)
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning