University Physics with Modern Physics, Books a la Carte Edition; Modified MasteringPhysics with Pearson eText -- ValuePack Access Card -- for ... eText -- Valuepack Access Card (14th Edition)
14th Edition
ISBN: 9780134308142
Author: Hugh D. Young, Roger A. Freedman
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Question
Chapter 40, Problem 40.65CP
(a)
To determine
The classical turning points for a harmonic oscillator with energy
(b)
To determine
To show: That Energy levels for the harmonic oscillator using
(c)
To determine
How do approximate energy levels
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Please asap
A simple harmonic oscillator is in the ground state with A-², where A=1/41/4 jm-1/2 and a = 1/2 m2, What is a (x²) and Ax? (Hint: [ [_xe-x²³ dx=0 and [_x²a-b²³dx==√m/6²³ )
Ax-
μm
m2
um
4.
a) Describe the Variational Principle
= e-ax?
b) The variation method is applied to a harmonic oscillator using a trial function = e
Minimize the energy as a function of the variable a.
k
The solution for energy is E =
24
8a
Leave your answer in terms of h, k, and u.
Compare your answer to the true energy of a harmonic oscillator, E =
v+) ha, where
v = 0,1,2, ... and w =
Chapter 40 Solutions
University Physics with Modern Physics, Books a la Carte Edition; Modified MasteringPhysics with Pearson eText -- ValuePack Access Card -- for ... eText -- Valuepack Access Card (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
- The wavelength of the emitted photon from the hydrogen molecule H2 is 2.30 μm (micrometers) when the vibrational quantum number decreases by one. What is the effective "spring constant" for the H2 molecule in N/m ?What is the "zero point" energy (in eV) of the molecular vibration?arrow_forwardAn electron is confined to move in the xy plane in a rectangle whose dimensions are Lx and Ly. That is, the electron is trapped in a two dimensional potential well having lengths of Lx and Ly. In this situation, the allowed energies of the electron depend on the quant numbers Nx and Ny, the allowed energies are given by E = H^2/8Me ( Nx^2/ Lx^2 + Ny^2/Ly^2) i) assuming Lx and Ly =L. Find the energies of the lowest for all energy levels of the electron ii) construct an energy level diagram for the electron and determine the energy difference between the second exited state and the ground state?arrow_forwardAs a 1-dimensional problem, you have Schrodinger's equation, given by: -h? a2 a ih h 4(x, t) = at 2m Əx² ¥(x,t) + V(x) Þ(x,t) Suppose for a specific V(x) and certain boundary conditions, the function w, (x, t) is a solution to the above equation and 42 (x, t) is also a solution. Show that (x, t) equation, where a, b are complex numbers. a 41 (x, t) + b w2(x, t) also solves the abovearrow_forward
- es The atoms of an FCC lattice are hard spheres touching the surfaces of the nearest neighbors. If the effective radius of atom is 4.25 Angstrom, what is the surface density in the (110) plane and what is the distance between nearest (110) planes. Select the correct response 138 x 10¹3 cm3 and 8.5 A 9.79 x 1013 cm3 and 8.5 A 315x 1014 cm3 and 4.74 A 196 x 10¹4 cm3 and 104 Aarrow_forwardThe position as a function of time x(t) of a simple harmonic oscillator is given by: x(t) = A cos(wt) %3D where A is the amplitude and w is the angular velocity. a) What is the range of possible values of x permitted for this oscillator? b) Derive the probability density function of p(x) for this oscillator. c) Validate that p(x) is normalized.arrow_forwardA non-isotropic harmonic oscillator has wi = W, W2 w, w2 = ;w, w3 = 2w. Its energy levels up to the fourth excited state level in terms of hw are Select one: О a. 1.75, 2.75, 3.75, 4.75, 5.75 Ob. Оь. 1.75, 2.5, 3.25, 4.0,4.5 с. 1.5,2.5, 3.5, 4.5,5.5 O d. 1.5, 1.75, 2.25, 3.5, 3.75 e. 1.75, 2.25, 2.75, 3.25, 3.75arrow_forward
- Suppose a system contain four identical particles and five energy levels given by the relationship, E;= i × 10-2º J, where i = 0,1,2 ,3,4. If the total energy of the system is Er= 6 E. Find the total number of the microscopic states for the distribution of these particles over the system energy levels keeping the given system conditions. Solution 4 identical particles Energy (10- Joule) Macroscopic state 4 Er= 6 € 3 Levels 1 E2 E (10-º J) k 1 2 4 5 6 7 N! Wk no! n!n2!n3!n4! Sk = kglnwkarrow_forwardSimplify the 1D phonon-dispersion relation such that it is in terms of the mass ratio ?=?2/?1.arrow_forwardSolid metals can be modeled as a set of uncoupled harmonic oscillators of the same frequency with energy levels given by En = ħwn n = 0, 1, 2,... where the zero-point energy (the lowest energy state) of each oscillator has been adjusted to zero for simplicity. In this model, the harmonic oscillators represent the motions of the metal atoms relative to one another. The frequency of these oscillators is low so that ħw = = 224 KB and the system vibrational partition function is given by 3N Z ² = la₁ - (1 1 e-0/T). (a) If the system contains one mole of atoms, find the average energy (in J) of this system at T= 172 K. (You can use = BkB.) T (b) What is the absolute entropy (in J/K) for this system? You can use either the Gibbs expression for S, or the system partition function to make this evaluation (they are equivalent, as your reading assignment indicates).arrow_forward
- Impurities in solids can be sometimes described by a particle-in-a-box model. Suppose He is substituted for Xe, and assume a particle-in-a-cubic-box model, the length of whose sides is equal to the atomic diameter of Xe (≈ 2.62 Å). Compute the lowest excitation energy for the He atom’s motion. (This is the energy difference between the ground state and the first excited state.)arrow_forwardA nitrogen molecule (N2) vibrates with energy identical to a single particle of mass m = 1.162 x 10-26 kg attached to a spring with a force constant of k = 1500 N/m. Suppose the energy levels of the system are uniformly spaced as shown in the figure below. The lowest energy level is often called the “ground state” and is assigned an integer value n = 1. The next higher energy level is often called the “first excited state” and is assigned an integer value n =2. (1) What is the vibration frequency of this molecule? (2) How much energy is required to excite the molecule from the ground state (n = 1) to the first excited state (n = 2)? (3) How much energy is required to excite the molecule from the first excited state (n = 2) to the state n = 5?arrow_forwardThe laboratory operation of a Laser is related to the atomic transition problem. Let E - E, = ho for two atomic states, u(@) be the radiation density, N be the number of atoms in state 1, and N2 that in state 2. B12 is the Enstein coffeicent for absorption, B21 that transition probability for emission, and A the spontaneous emission coefficient. Find N2/N1 O B12/[A+ B21] O B1zu(@)/[A + B21u(@)] O B1zu(@)/A O B1zu(@)/B21 O Au(@)/B12 Questio Not yet answered Marked out of P Flag question Forbidden transitions and selection rules suggest that O a photon has energy O a photon has mass O a photon has linear momentum O a photon has angular momentum a photon has parityarrow_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 LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher: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