University Physics with Modern Physics (14th Edition)
14th Edition
ISBN: 9780321973610
Author: Hugh D. Young, Roger A. Freedman
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Question
Chapter 40, Problem 40.9DQ
To determine
To explain: Whether it is possible to represent the wave function of a particle in a box as a combination of two standing waves and the physical interpretation of this representation.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Hi there, I would just like to ask the Copenhagen interpretation of Light that is both as a particle and a wave and would like to verify if I understand it right. So basically Light exists as both a particle and a wave but we'll only know what state it is in when we test it or we won't know what state it will be unless we open the box (in reference to Schrodingers thought experiment). Because before diving to the quantum mechanics interpretation of light, I thought of it as a particle moving in a wave but since both cannot exist at the same time or at least it would bend our understanding of the two. I would like to receive some enlightenment thank you!
2. Consider a system with Neumann boundary conditions. Show that the Neumann Green's
function is symmetric under exchange of its two position variables i.e.
Gr(7,7") = Gy(", 5).
GN(F,")
. Is it possible for the de Broglie wavelength of a “particle”to be greater than the dimensions of the particle? To besmaller? Is there any direct connection? Explain.
Chapter 40 Solutions
University Physics with Modern Physics (14th Edition)
Ch. 40.1 - Does a wave packet given by Eq. (40.19) represent...Ch. 40.2 - Prob. 40.2TYUCh. 40.3 - Prob. 40.3TYUCh. 40.4 - Prob. 40.4TYUCh. 40.5 - Prob. 40.5TYUCh. 40.6 - Prob. 40.6TYUCh. 40 - Prob. 40.1DQCh. 40 - Prob. 40.2DQCh. 40 - Prob. 40.3DQCh. 40 - Prob. 40.4DQ
Ch. 40 - If a panicle is in a stationary state, does that...Ch. 40 - Prob. 40.6DQCh. 40 - Prob. 40.7DQCh. 40 - Prob. 40.8DQCh. 40 - Prob. 40.9DQCh. 40 - Prob. 40.10DQCh. 40 - Prob. 40.11DQCh. 40 - Prob. 40.12DQCh. 40 - Prob. 40.13DQCh. 40 - Prob. 40.14DQCh. 40 - Prob. 40.15DQCh. 40 - Prob. 40.16DQCh. 40 - Prob. 40.17DQCh. 40 - Prob. 40.18DQCh. 40 - Prob. 40.19DQCh. 40 - Prob. 40.20DQCh. 40 - Prob. 40.21DQCh. 40 - Prob. 40.22DQCh. 40 - Prob. 40.23DQCh. 40 - Prob. 40.24DQCh. 40 - Prob. 40.25DQCh. 40 - Prob. 40.26DQCh. 40 - Prob. 40.27DQCh. 40 - Prob. 40.1ECh. 40 - Prob. 40.2ECh. 40 - Prob. 40.3ECh. 40 - Prob. 40.4ECh. 40 - Prob. 40.5ECh. 40 - Prob. 40.6ECh. 40 - Prob. 40.7ECh. 40 - Prob. 40.8ECh. 40 - Prob. 40.9ECh. 40 - Prob. 40.10ECh. 40 - Prob. 40.11ECh. 40 - Prob. 40.12ECh. 40 - Prob. 40.13ECh. 40 - Prob. 40.14ECh. 40 - Prob. 40.15ECh. 40 - Prob. 40.16ECh. 40 - Prob. 40.17ECh. 40 - Prob. 40.18ECh. 40 - Prob. 40.19ECh. 40 - Prob. 40.20ECh. 40 - Prob. 40.21ECh. 40 - Prob. 40.22ECh. 40 - Prob. 40.23ECh. 40 - Prob. 40.24ECh. 40 - Prob. 40.25ECh. 40 - Prob. 40.26ECh. 40 - Prob. 40.27ECh. 40 - Prob. 40.28ECh. 40 - Prob. 40.29ECh. 40 - Prob. 40.30ECh. 40 - Prob. 40.31ECh. 40 - Prob. 40.32ECh. 40 - Prob. 40.33ECh. 40 - Prob. 40.34ECh. 40 - Prob. 40.35ECh. 40 - Prob. 40.36ECh. 40 - Prob. 40.37ECh. 40 - Prob. 40.38ECh. 40 - Prob. 40.39ECh. 40 - Prob. 40.40ECh. 40 - Prob. 40.41ECh. 40 - Prob. 40.42PCh. 40 - Prob. 40.43PCh. 40 - Prob. 40.44PCh. 40 - Prob. 40.45PCh. 40 - Prob. 40.46PCh. 40 - Prob. 40.47PCh. 40 - Prob. 40.48PCh. 40 - Prob. 40.49PCh. 40 - Prob. 40.50PCh. 40 - Prob. 40.51PCh. 40 - Prob. 40.52PCh. 40 - Prob. 40.53PCh. 40 - Prob. 40.54PCh. 40 - Prob. 40.55PCh. 40 - Prob. 40.56PCh. 40 - Prob. 40.57PCh. 40 - Prob. 40.58PCh. 40 - Prob. 40.59PCh. 40 - Prob. 40.60PCh. 40 - Prob. 40.61PCh. 40 - Prob. 40.62PCh. 40 - Prob. 40.63PCh. 40 - Prob. 40.64CPCh. 40 - Prob. 40.65CPCh. 40 - Prob. 40.66CPCh. 40 - Prob. 40.67PPCh. 40 - Prob. 40.68PPCh. 40 - Prob. 40.69PPCh. 40 - Prob. 40.70PP
Knowledge Booster
Similar questions
- Is it possible that when we measure the energy of a quantum particle in a box, the measurement may return a smaller value than the ground state energy? What is the highest value of the energy that we can measure for this particle?arrow_forwardIs it possible to measure energy of 0.75h for a quantum harmonic oscillator? Why? Why not? Explain.arrow_forward3. A particle of mass m moves in one dimension in a potential given by v(s)-c). where 8() is the Dirac delta function. The particle is bound. Find the value , such that the probability of finding the particle with l<, is exactly 1/2.arrow_forward
- For a particle in a box, what would the probability distribution function Ic I2 look like if the particle behaved like a classical (Newtonian) particle? Do the actual probability distributions approach this classical form when n is very large? Explain.arrow_forwardAre the following phenomena wave or particle behaviors? Give your reasoning. (a) Television picture, (b) rainbows, (c) football sailing between goal posts, (d) telescope observing the moon, (e) police radararrow_forward4. For parts a, b, c state whether the given wavefunction is admissible or not and justify your answer. (a) Given y (x, t) = Cei(kx-wt) + Cze-i(kx+wt) with C1 and C2 complex numbers and k real. (b) Given 4 (x, t) = A cos(@t) e-blal with A and b real, and b > 0. (c) Given (x, t) = Ce-iwte-alx| for -o 0. (d) Sketch the probability density associated with the wavefunction p(x, t) defined in part (c).arrow_forward
- 16. A particle has the following wavefunction: L) from x = 0 to x = L, and y everywhere else. Ax(x (a) What is the value of A? (b) What is the probability of finding the particle in the region 0 < x < L/2? (You can calculate this, but you can also figure it out with no calculations by making a graph.) - = = 0 (c) What is the probability of finding the particle in the region 0 < x < L/4? (This one you have to calculate, although a graph can be a great reality check.)arrow_forward1) An electron is confined to a square box of length L, and the walls of that box are infinitely high. The zero-point energy (ZPE) is defined as the minimal energy that corresponds to the smallest quantum number n. What would be the length of the box L such that the ZPE of the electron located inside this box is equal to its rest mass energy mec2?arrow_forwardIn order to solve the Schrödinger equation, one needs to apply boundary conditions. Which of the following best describe what is meant by boundary conditions in this context? The values of the wave function and its time derivative at t=0. The values of the wave function and its spatial derivatives at t=0. The functional form of the potential, V(r). The continuity both the first and second derivatives of the time derivatives. E The continuity of the wave function and its spatial derivatives at a boundary between regions of different potentials, V(r).arrow_forward
- 1. A particle of mass m is in the state Y(r, t) = Ac 25 = Ac 25 where A and w are positive real constants and i= v-1. For what time-intependent potential energy function V(x) does Y satisfy the Schrödinger equation for a particle of mass m? (Simply plug the Y you are given into the time-dependent Schrödinger equation: h a?¥(x,t) aY(x,t) ih at +V(x)¥(x,t) , 2m take the space and time derivatives and solve for V(x).]arrow_forward2. Suppose a particle of mass, m, has energy E, and wave function: WE (x, t = 0) = Aeikx + Be-ikx What is WE(x, t)? Calculate the probability density of the particle when it has the wavefunction, E (x, t). If you wish to simply your answer algebraically, use this information: let A = aeia and B = beif and A = a - B. where the variables a, b, a, ß are all real! WARNING: Simplifying the equation is somewhat time consuming. Show/explain why p(x,t) is not normalizable. According to quantum theory, all physical systems must have an associated wavefunction that is normalizable. Explain why plane wave solutions to Schrodinger's equation are used in quantum theory, despite not being normalizable?arrow_forwardA particle is created in a shower of particle decays. Its velocity is measured to a precision of 50 micrometers/second and its mass is inferred to be (exactly) 6.64×10−27 kg. What is the minimum uncertainty in our knowledge of the particle’s position? Explain.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 LearningUniversity Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStaxModern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning
Physics for Scientists and Engineers with Modern ...
Physics
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
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