Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Question
Chapter 40, Problem 25P
(a)
To determine
To normalize the wave function for the ground state of a simple harmonic oscillator.
(b)
To determine
The probability of finding the oscillator in a narrow interval of
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
The properties of the GaAs quantum well in the figure are as follows.
V0 = 100 meV L = 200 Å m∗ = 0.067 me
Find the energy values of the first three levels of this well using the finite difference method. Plot the corresponding wave functions. Effective mass m ∗ given for the well Agree that it also applies to barriers. The material of the barrier is not important here. Important is the V0 potential.
prove :
a) Separable solutions to the (time-dependent Schrödinger equation ) lead to stationary stats.
b) stationary states have definite energy .
What is the answer
Chapter 40 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 40.1 - Prob. 40.1QQCh. 40.2 - Prob. 40.2QQCh. 40.2 - Prob. 40.3QQCh. 40.5 - Prob. 40.4QQCh. 40 - Prob. 1PCh. 40 - Prob. 2PCh. 40 - Prob. 3PCh. 40 - Prob. 4PCh. 40 - Prob. 5PCh. 40 - Prob. 6P
Ch. 40 - Prob. 7PCh. 40 - Prob. 9PCh. 40 - Prob. 10PCh. 40 - Prob. 11PCh. 40 - Prob. 12PCh. 40 - Prob. 13PCh. 40 - Prob. 14PCh. 40 - Prob. 15PCh. 40 - Prob. 16PCh. 40 - Prob. 17PCh. 40 - Prob. 18PCh. 40 - Prob. 19PCh. 40 - Prob. 20PCh. 40 - Prob. 21PCh. 40 - Prob. 23PCh. 40 - Prob. 24PCh. 40 - Prob. 25PCh. 40 - Prob. 26PCh. 40 - Prob. 27PCh. 40 - Prob. 28PCh. 40 - Prob. 29PCh. 40 - Two particles with masses m1 and m2 are joined by...Ch. 40 - Prob. 31APCh. 40 - Prob. 32APCh. 40 - Prob. 33APCh. 40 - Prob. 34APCh. 40 - Prob. 36APCh. 40 - Prob. 37APCh. 40 - Prob. 38APCh. 40 - Prob. 39APCh. 40 - Prob. 40APCh. 40 - Prob. 41APCh. 40 - Prob. 42APCh. 40 - Prob. 44CPCh. 40 - Prob. 46CPCh. 40 - Prob. 47CP
Knowledge Booster
Similar questions
- The Einstein's model makes the assumption that a solid can be treated a set of N identical, independent harmonic oscillators. Compute the heat capacity for such a system. Make the simplifying assumption that a single harmonic oscillator is described by the quantized energy levels: Ek=kℏω, where k=0,1,2,….arrow_forwardA proton is confined in box whose width is d = 750 nm. It is in the n = 3 energy state. What is the probability that the proton will be found within a distance of d/n from one of the walls? [Hint: the average value sin2x over one or more of its cycles is 1/2.] Include a sketch of U(x) and ?(x).arrow_forwardConsider a particle moving in a one-dimensional box with walls at x = -L/2 and L/2. (a) Write the wavefunction and probability density for the state n=1. (b) If the particle has a potential barrier at x =0 to x = L/4 (where L = 10 angstroms) with a height of 10.0 eV, what would be the transmission probability of the electrons at the n = 1 state? (c) Compare the energy of the particle at the n= 1 state to the energy of the oscillator at its first excited state.arrow_forward
- A particle is in a three-dimensional box. The y length of the box is twice the x length, and the z length is one-third of the y length. (a) What is the energy difference between the first excited level and the ground level? (b) Is the first excited level degenerate? (c) In terms of the x length, where is the probability distribution the greatest in the lowest-energy level?arrow_forward15 6x4 – 12Lx³ + 15 L²x? - 3,3 (- L²r? L3x 6r4 - N2 2me 12La3 dx = dx 2 2 2 Evaluate the integral in the numerator. p*H@ dx = N² 40m h² L³ e 40me The denominator of the E expression from Step 1 is 6 _ 3Lx + 13 ,2 4 -L²x 4 Lx³ + F8-3Lz' + 12rt - (%) Lz3 + +L교2 p dx = N² dx Evaluate the integral in the denominator. 1 1 φ φ αχx = N2 840 840 Step 3 of 6 Divide the numerator by the denominator (both from Step 2) and simplify. (Use the following as necessary: ħ, L, me, P, T, and x.) 21h? E L²m 21h? L²me e Step 4 of 6 Calculate the energy for an electron in a 0.43-nm box using the formula from Step 3. = 4.0 0.26 X 840 kJ•mol-1 φ Step 5 of 6 Calculate the exact energy for an electron in the first excited state in a 0.43-nm box. n2h2 Recall that for a particle in a one-dimensional box we can write En we can therefore calculate an exact solution. 8mL2' Eexact = 4.0 197 X kJ-mol-1 Submitarrow_forwardhelp with modern physics questionarrow_forward
- An electron is in an infinite potential well of width 364 pm, and is in the normalised superposition state Ψ=cos(θ) ψ5-sin(θ) i ψ8. If the value of θ is -1.03 radians, what is the expectation value of energy, in eV, of the electron?arrow_forwardConsider a heat reservoir at temperature T is in contact with a one-dimensional quantum oscillator whose vibrational frequency is . Calculate the ratio of the probability of the oscillator that exists in the first excited state and to the ground state. Answer Choices: a. e b. e C. d. -(1) e no 2kgT e 2.000 32 Tarrow_forwardHere are the properties of the GaAs quantum well in the figure. v0 = 100 ??? L = 200 Å ?∗ = 0.067 m* Find the energy values of the first three levels of this well. Corresponding wave functions Draw the graph. It is assumed that the effective mass m* given for the well is also valid for barriers. please. The material of the barrier is not important here. The important thing is the V0 potential.arrow_forward
- A wave function has the value A sin x between x= 0 and π but zero elsewhere. Normalize the wave function and find the probability that the particle is (a) between x = 0 and x = π/4 and (b) between x= 0 and π/2.arrow_forwardA O, molecule oscillates with a frequency of 4.7 x1013 Hz. (a) What is the difference in energy in ev between allowed oscillator states? ev (b) what is the approximate value of n for a state having an energy of 1.4 eV? (Give your answer to the nearest integer.)arrow_forwardConsider a particle in a box of length L= 1 for the n= 2 state. The wave function is defined as: (x) = sin (27x) %3| Normalize the wave function.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
Modern 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
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning