Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
expand_more
expand_more
format_list_bulleted
Question
Chapter 5, Problem 96CE
To determine
To Show:Potential energy is
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
A 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 3mhw
A particle with mass m is moving in three-dimensions under the potential energy U(r), where
r is the radial distance from the origin. The state of the particle is given by the time-independent
wavefunction,
Y(r) = Ce-kr.
Because it is in three dimensions, it is the solution of the following time-independent
Schrodinger equation
dıp
r2
+ U(r)µ(r).
dr
h2 d
EÞ(r) =
2mr2 dr
In addition,
00
1 =
| 4ar?y? (r)dr,
(A(r)) = | 4r²p²(r)A(r)dr.
a. Using the fact that the particle has to be somewhere in space, determine C. Express your
answer in terms of k.
b. Remembering that E is a constant, and the fact that p(r) must satisfy the time-independent
wave equation, what is the energy E of the particle and the potential energy U(r). (As
usual, E and U(r) will be determined up to a constant.) Express your answer in terms of
m, k, and ħ.
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
- A particle with mass m is in the state тс V (x,t) = Ae +iat 2h where A and a are positive real constants. Calculate the potential energy function that satisfies the Schrodinger equation.arrow_forwardConsider an anisotropic 3D harmonic oscillator where we = Wy the energy of the particle in the following state (nx, ny, n₂) = (0, 0, 2)? = w and wz A. 4ħw B. 6hw C. 3ħw D. 2.5ħw = 2w. What isarrow_forwardA particle is confined in a box of length L as shown in the figure. If the potential is treated as a perturbation, including the first order correction, the ground state energy is (a) E = ħ²π² 2mL² + V (b) E = ħ²π² Vo 2mL² ħ²π² Vo ħ²π² Vo (c) E = + (d) E = + 2mL² 4 2mL² L/2arrow_forward
- A system of three identical distinguishable particles has energy 3ɛ. The single particle can take discrete energies 0, &, 2, 3ɛ and so on. The average number of particles in the energy state & is 1.2 0.9 0.6 0.3arrow_forwardThe general solution of the Schrodinger equation for a particle confined in an infinite square-well potential (where V = 0) of width L is w(x)= C sin kx + Dcos kx V2mE k where C and D are constants, E is the energy of the particle and m is the mass of the particle. Show that the energy E of the particle inside the square-well potential is quantised.arrow_forwardU = U, %3D U = 0 X = 0 A potential step U(x) is defined by U(x) = 0 for x 0 If an electron beam of energy E > U, is approaching from the left, write the form of the wave function in region I (x 0) in terms of the electron mass m, energy E, and potential energy U,. Do not bother to determine the constant coefficients. Formulas.pdf (Click here-->) Edit Vicw Insert Format Tools Table 12pt v Paragraph BIU Av eu T? varrow_forward
- +8 x a nd described by the wave function y(x)= Bsin(kx). Determine i) The energy levels, the omentum, the wave length, the parity and number of nodes for the states n = 1, 2 3 and 4. Suppose V=10 J in the box. What effect has this on a) eigenvalues? b) the eigen functions?arrow_forwardSolving the Schrödinger equation for a particle of energy E 0 Calculate the values of the constants D, C, B, and A if knownCalculate the values of the constants D, C, B, and A if known and 2mE 2m(Vo-E) a =arrow_forwardA particle with mass m is in a field and has the state (in spherical coordinates) : Where N > 0 and a > 0 are fixed numbers. Determine the average kinetic energy of the particles.arrow_forward
- A particle of mass m is subjected to a force F(r) = -VV(r) such that the wave function p(p, t) satisfies the momentum-space Schrödinger equation %3D (p²/2m – aV,) p(p, t) = idp(p, t)/ôt, %3D where h = 1, a is some real constant and V; = /dp? + 8² /əp", + a² /ðp? . Find the force F (r).arrow_forwardA particle of mass 1.60 x 10-28 kg is confined to a one-dimensional box of length 1.90 x 10-10 m. For n = 1, answer the following. (a) What is the wavelength (in m) of the wave function for the particle? m (b) What is its ground-state energy (in eV)? eV (c) What If? Suppose there is a second box. What would be the length L (in m) for this box if the energy for a particle in the n = 5 state of this box is the same as the ground-state energy found for the first box in part (b)? m (d) What would be the wavelength (in m) of the wave function for the particle in that case? marrow_forwardHarmonic oscillator eigenstates have the general form 1 μω ,1/4 μω AG)(√(-) n ħ In this formula, which part determines the number of nodes in the harmonic oscillator state? = y (x) 1 √(™ ћn 2"n! Holev 1/4 μω 1 2"n! exp(-1022²) 2ħ μω ħ 2"n! exp μω χ 2ħ 2arrow_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 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
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning