Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
expand_more
expand_more
format_list_bulleted
Question
Chapter 5, Problem 32E
To determine
To Show:
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
At time t = 0 the normalized wave function for a particle of mass m in the one-dimensional infinite well (see first image) is given by the function in the second image.
Find ψ(x, t). What is the probability that a measurement of the energy at time t will yield the result ħ2π2/2mL2? Find <E> for the particle at time t. (Hint: <E> can be obtained by inspection, without an integral)
consider an infinite square well with sides at x= -L/2 and x = L/2 (centered at the origin). Then the potential
energy is 0 for [x] L/2 Let E be the total energy of the particle.
=0
(a) Solve the one-dimensional time-independent Schrodinger equation to find y(x) in each region.
(b) Apply the boundary condition that must be continuous.
(c) Apply the normalization condition.
(d) Find the allowed values of E.
(e) Sketch w(x) for the three lowest energy states.
(f) Compare your results for (d) and (e) to the infinite square well (with sides at x=0 and x=L)
Consider a potential barrierV(x) = {0, xVo, find the
transmission coefficient, T
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
- An electron having total energy E = 4.50 eV approaches a rectangular energy barrier with U = 5.00 eV and L = 950 pm as shown. Classically, the electron cannot pass through the barrier because E < U. Quantum- mechanically, however, the probability of tunneling is not zero. (a) Calculate this probability, which is the transmission coefficient. (b) To what value would the width L of the potential barrier have to be increased for the chance of an incident 4.50-eV electron tunneling through the barrier to be one in one million?arrow_forwardConsider the first excited state of the quantum harmonic oscillator (v = 1) and the wavefunction P₁(x), with a = 0.1 m, (a nonphysical but convenient value). a) Show that ₁(x) is normalized.arrow_forwardA particle of mass m is trapped in a three-dimensional rectangular potential well with sides of length L, L/ √2, and 2L. Inside the box V = 0, outside V = ∞. Assume that Ψ = Asin (k1x) sin (k2y) sin (k3z) inside the well. Substitute this wave function into the Schrödinger equation and apply appropriate boundary conditions to find the allowed energy levels. Find the energy of the ground state and first four excited levels. Which of these levels are degenerate?arrow_forward
- Using the time-independent Schrödinger equation, find the potential V(x) and energy E for which the wave function y(x): where n, x are constants, is an eigenfunction. Assume that V(x) → 0 as x → 0.arrow_forwardA Quantum Harmonic Oscillator, with potential energy V(x) = ½ mω02x2, where m is the mass of the particle in the potential, and ω0 is a constant.Show that the following wavefunction provided satisfies the one-dimensional time-independent Schrodinger ¨equation of this system, for a certain value of E.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_forward
- Use the time-dependent Schroedinger equation to calculate the period (in seconds) of the wavefunction for a particle of mass 9.109×10−31 kg in the ground state of a box of width 1.2×10−10 m.arrow_forwardThe following Eigen function is a typical solution of the time-independent Schrödinger equation and satisfies boundary conditions for a particle in a confined space of a certain length. y(x) = sin (~77) (a) Plot the wave function as a function of x for L = 30 cm and n = 1, 2, 3 and 4. Note: You will need to have 4 plots in the same graph. (b) On a separate graph, plot the probability density (112) as a function of x using the conditions specified in part (a). Note: You will need to have 4 plots in the same graph. (c) Report your observations for parts (a) and (b)arrow_forwardProperty 2 of the boundary conditions for wave functions specifies that Ψ must be continuous in order to avoid discontinuous probability values. Why can’t we have discontinuous probabilities?arrow_forward
- The wavefunction for v =1 for a simple harmonic oscillator is Ψ = (2)1/2 ( α3/π)1/4 x exp (-αx2/2) Find the values of x such that ψ* ψ is a maximum.Hint: Differentiate dψ*ψ/dx and set the result equal to zero and solve for the value of x.arrow_forwardIf a particle is completely free to move with no restrictions, the potential energy is 0everywhere. One solution to this free particle in one dimension isψ(x) = ei√2mE/~x. Show that this wave function satisfies the Schrodinger Equation.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
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 Learning
Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher: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 with Modern ...
Physics
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning