Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
expand_more
expand_more
format_list_bulleted
Question
Chapter 5, Problem 22E
To determine
To Show:Thestanding-wave function of the infinite well can be expressed as sum of two traveling waves.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
The odd parity eigenstates of the infinte square well , with potential V = 0 in the range −L/2 ≤ x ≤ L/2, are given by :
(see figure)
and have Ψn(x, t) = 0 elsewhere , for n=2 , 4 , 6 etc
I have got the expectation value of momentum for ⟨p⟩ and ⟨p 2⟩ for n = 2 (see figures)
By direct substitution, show that the wavefunction in the figure satisfies the timedependent Schrodinger equation (provided that En takes the value derived in figure).
Try to normalize the wave function ei(kx-ωt) . Why can’t it be done over all space? Explain why this is not possible
Solve the following.
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
- Physics Consider particles of mass "m" in an infinite square well (a box) of size "L". a. Write the wave function for a situation in which the particles are in a superposition of state "s" with energies E5, E6, E8 with probabilities P(E5) =P(E6) =1/4. b. Write explicitly the integral needed to calculate in order to find the average value of the position operator < X >. No need to calculate the integrals explicitly.arrow_forward6QM Please answer question throughly and detailed.arrow_forwardConsider an infinite well, width L from x=-L/2 to x=+L/2. Now consider a trial wave-function for this potential, V(x) = 0 inside the well and infinite outside, that is of the form (z) = Az. Normalize this wave-function. Find , .arrow_forward
- A ID harmonic oscillator of angular frequency w and charge q is in its ground state at time t=0. A perturbation H'(t) = qE eA3 (where E is ekctric field and ß is a constant) is %3D applied for a time t = t. Cakulate the probability of transition to the first and second excited state. (hint: you may expand exponential in perturbation and keep it only up to linear term)arrow_forwardQuestion A6 Consider an infinite square well with V = 0 in the interval -L/2 < x < L/2, and V → ∞ everywhere else. A particle of mass m is in the groundstate of this system, and is known to have a wavefunction and energy given by TX √ = COS and E = π²h² 2mL² The system is then perturbed so that its potential takes the constant value Varrow_forwardThe normalised wavefunction for an electron in an infinite 1D potential well of length 80 pm can be written:ψ=(0.587 ψ2)+(0.277 i ψ7)+(g ψ6). As the individual wavefunctions are orthonormal, use your knowledge to work out |g|, and hence find the expectation value for the energy of the particle, in eV.arrow_forwardA quantum mechanical particle is confined to a one-dimensional infinite potential well described by the function V(x) = 0 in the region 0 < x < L, V(x) = ∞ elsewhere. The normalised eigenfunctions for a particle moving in this potential are: Yn(x) = √ 2 Nπ sin -X L L where n = 1, 2, 3, .. a) Write down the expression for the corresponding probability density function. Sketch the shape of this function for a particle in the ground state (n = 1). b) Annotate your sketch to show the probability density function for a classical particle moving at constant speed in the well. Give a short justification for the shape of your sketch. c) Briefly describe, with the aid of a sketch or otherwise, the way in which the quantum and the classical probability density functions are consistent with the correspondence principle for large values of n.arrow_forwardFor an electron in a one-dimensional box of width L (x lies between 0 and L), (a)Write down its wavefunction and the allowed energy. (b)If the electron is in a superposition of the ground state and second excited state, write down the wavefunction and compute the probability of finding the electron at 1/6 ?. (Don’t forget to normalize it!)arrow_forwardhelp with modern physics questionarrow_forwardThe wave function for the first excited state y, for the simple harmonic oscillator is y, = Axe (ax-/2), Normalize the wave function to find the value of the constant A. (Use the following as necessary: a) A%3D Determine (x), (x-), and y (x2) - (x)². (Use the following as necessary: a) (x) (x?) V (x?) - (x)? : Need Help? Read Itarrow_forwardConsider an electron in a one-dimensional, infinitely-deep, square potential well of width d. The electron is in the ground state. (a) Sketch the wavefunction for the electron. Clearly indicate the position of the walls of the potential well on your sketch. (b) Briefly explain how the probability distribution for detecting the electron at a given position differs from the wavefunction.arrow_forwardConsider the wave function for the ground state harmonic oscillator: m w1/4 e-m w x2/(2 h) A. What is the quantum number for this ground state? v = 0 B. Enter the integrand you'd need to evaluate (x) for the ground state harmonic oscillator wave 'function: (x) = |- то dx e C. Evaluate the integral in part B. What do you obtain for the average displacement? 0arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
Recommended textbooks for you
- Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage LearningModern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning