Modified Mastering Physics with Pearson eText -- Combo Access -- for Physics for Scientist and Engineers (18 week)
5th Edition
ISBN: 9780137504299
Author: Douglas C. Giancoli
Publisher: Pearson Education (US)
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 38, Problem 18P
(a)
To determine
The proof that function
(b)
To determine
The proof that conservation of energy gives the result
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
(2nx
sin
\1.50.
2nz
Consider the case of a 3-dimensional particle-in-a-box. Given: 4 =
sin(ny) sin
2.00.
What is the energy of the system?
O 6h?/8m
O 4h²/8m
O 3h2/8m
O none are correct
For the scaled stationary Schrödinger equation "(x) + 8(x)v(x) = Ev(x),
find the eigenvalue E and the wave function ý under the constraint
/ »(x)²dx = 1.
(a) Calculate the energy separations in units of joules and kilojoules per mole, respectively, between thelevels n = 2 and n = 1 of an electron in a one-dimensional box of length 1.0 nm.
(b) Calculate the zero point energy of a harmonic oscillator consisting of a particle of mass 2.33 × 10−26 kgwith a force constant 155 N m−1.
Chapter 38 Solutions
Modified Mastering Physics with Pearson eText -- Combo Access -- for Physics for Scientist and Engineers (18 week)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- An electron is confined in the ground state of a one-dimensional har- monic oscillator such that V((r – (x))²) = 10-10 m. Find the energy (in eV) required to excite it to its first excited state. (Hint: The virial theorem can help.]arrow_forwardThe radial function of a particle in a central potential is give by wave [ - r R(r) = A-exp where A is the normalization constant and a is positive constant еxp а 2a of suitable dimensions. If ya is the most probable distance of the particle from the force center, the value of y isarrow_forward(a) Show that the linear combination ‚E2 P(x, t) = 4; (x)e¯ +¥½(x)e¬l*t is a solution of the time-dependent Schrödinger equation, provided that the function W1 (x) and 2(x) are solutions of the time-independent Schrödinger equation with E = E, and E E2, respectively.arrow_forward
- (1) For the helium-neon laser, estimate the Doppler broadening of the output wavelength 632.8 nm at T= 293 K. (2) Estimate the broadening of the same wavelength due to the Heisenberg uncertainty principle, assuming that the metastable state has a lifetime of about 1 ms.arrow_forward2) Consider a particle in a three-dimensional harmonic oscillator potential V (r, y, z) = 5mw²(r² + y² + z®). The stationary states of such a system are given by ntm(r, y, z) = vn(x)¢r(y)v'm(2) (where the functions on the right are the single-particle harmonic oscillator stationary states) with energies Entm = hw(n +l+m+ ). Calculate the lifetime of the state 201.arrow_forwardA particle of massm in a harmonic oscillator potential with angular frequency w is in the state (1 + {t)쭈 What is (p?) for this particle? mhw 2 O 6mħw O 3mhwarrow_forward
- The wavefunction ψ[x] = A x^2 e^(- x/x0) where x0 is a constant, is defined in the region, 0 ≤ x ≤ ∞.(a) Determine the normalization constant, A(b) Using the definition Δx = (⟨x^2⟩ -⟨x⟩^2)^.5 determine Δx(c) Using the momentum operator -(ⅈ (h/2pi))(∂/∂x)determine ⟨p⟩ and ⟨p^2⟩(d) Determine Δp from the results obtained in (c) and evaluate Δx Δparrow_forwardYou have the energy matrix for only 4x4 elements. Calculate the expected value of energy (E) using the function 1 1 -fox /2 e -3icut 2 [e heo S 0 0 0 2 E= = 5 0 0 e 0 2 0 0 0 Ther 2 J Al Laxities (E) A8l 2 gidd) dasll Cuaal l o |2 l Jiew /2 Vi *[fi“ e 0:‘ 5arrow_forwardA particle of is mass moving in V (x,y,z) =mo (5x² +2y²). Determine the energy of the anisotropic oscillator in the m 1 a two-dimensional potential ground state. 3 (a) (15 – J2) ħo (b) (\5 +V2)ħo 21 (c) ħw 3. (d)(5 + V2 )ho (1)arrow_forward
- 3) Consider the collection of identical harmonic oscillators (as in the Einstein floor). The permitted energies of each oscilator (E = nhf (n=0, 1, 2.0, hf. 2hf and so on. a) Calculate the splitting function of a single harmonic oscitor. What is the splitting function of N oscilator? wwww wwwwww www www b) Obtain the average energy of the T-temperature N oscilator from the split function. c) Calculate the heat capacity of this system and T → 0 ve T → 0 in limits, what is the heat capacity of the system? Are these results in line with the experiment? Why? What's the right theory about that? w w d) Find the Helmholtz free energy of this system. www ww e) which gives the entropy of this system as a function of temperature. ww wd wwww wwarrow_forwardA particle is described by the wave function [V5 cos 0 + sin(e + 4) + sin(0 – ø)], 2/3n (a) Express 4(0, 4) in terms of spherical harmonics (b) Calculate p and Lzµ. Is y an eigenstate of I? and L,? (c) Calculate Î44 and (L4) If the measurement of Î, is carried out, find the probability of getting the results 0,ħ and -ħ. (d)arrow_forwardi) Why does the plane wave [Y(x,t)=Ae^i(kxewt)] have an issue and how to solve it? ii) What are the limitations of the time-dependent Schroedinger Equation?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningClassical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
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
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning