Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
expand_more
expand_more
format_list_bulleted
Question
Chapter 7.3, Problem 7.22P
To determine
To show that
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
post
|Consider a system which is in the state,
Y(0,4) =Y,"(0,ø)+ J¿r,"(0,ø)+Y'(0,$),
where Y," (0,4) are the spherical harmonics. If Î, is measured what possible values can
be obtained?
(a) –ħ,0,ħ
(b) +ħ‚2ħ,-ħ
(c) +ħ,3ħ,-ħ
(d) +ħ,-ħ
(е) 3h, 2h
if the chlorine molecule at 290K were to rotate at the angular frequency predicted by the equipartition theorem what would be the average centipital force ? ( the atoms of Cl are 2 x 10-10 m apart and the mass of the chlorine atom 35.45 a.m.u )
13.10 If the radial momentum p, and radial velocity a, for an electron in a central potential are
defined by
r.p-ih
a.r
Pr =
Xr=
"
r
r
show that
ihk Ba,
(ap) = ar Pr +
r
B(o'. L + h)
where k =
ħ
Chapter 7 Solutions
Introduction To Quantum Mechanics
Ch. 7.1 - Prob. 7.1PCh. 7.1 - Prob. 7.2PCh. 7.1 - Prob. 7.3PCh. 7.1 - Prob. 7.4PCh. 7.1 - Prob. 7.5PCh. 7.1 - Prob. 7.6PCh. 7.2 - Prob. 7.8PCh. 7.2 - Prob. 7.9PCh. 7.2 - Prob. 7.10PCh. 7.2 - Prob. 7.11P
Ch. 7.2 - Prob. 7.12PCh. 7.2 - Prob. 7.13PCh. 7.3 - Prob. 7.15PCh. 7.3 - Prob. 7.16PCh. 7.3 - Prob. 7.17PCh. 7.3 - Prob. 7.18PCh. 7.3 - Prob. 7.19PCh. 7.3 - Prob. 7.20PCh. 7.3 - Prob. 7.21PCh. 7.3 - Prob. 7.22PCh. 7.4 - Prob. 7.23PCh. 7.4 - Prob. 7.24PCh. 7.4 - Prob. 7.25PCh. 7.4 - Prob. 7.26PCh. 7.4 - Prob. 7.27PCh. 7.4 - Prob. 7.28PCh. 7.4 - Prob. 7.29PCh. 7.5 - Prob. 7.31PCh. 7.5 - Prob. 7.32PCh. 7 - Prob. 7.33PCh. 7 - Prob. 7.34PCh. 7 - Prob. 7.35PCh. 7 - Prob. 7.36PCh. 7 - Prob. 7.37PCh. 7 - Prob. 7.38PCh. 7 - Prob. 7.39PCh. 7 - Prob. 7.40PCh. 7 - Prob. 7.42PCh. 7 - Prob. 7.43PCh. 7 - Prob. 7.44PCh. 7 - Prob. 7.45PCh. 7 - Prob. 7.46PCh. 7 - Prob. 7.47PCh. 7 - Prob. 7.49PCh. 7 - Prob. 7.50PCh. 7 - Prob. 7.51PCh. 7 - Prob. 7.52PCh. 7 - Prob. 7.54PCh. 7 - Prob. 7.56PCh. 7 - Prob. 7.57P
Knowledge Booster
Similar questions
- !) given a line charge distribution of (102 C/m) on z axis, find VAB where A(3, 1/2,1) and B(4, z, 6).arrow_forwardConsider a simple model of the helium atom in which two electrons, each with mass m, move around the nucleus (charge +2e) in the same circular orbit. Each electron has orbital angular momentum U (that is, the orbit is the smallest-radius Bohr orbit), and the two electrons are always on opposite sides of the nucleus. Ignore the effects of spin. What is the potential energy of the system (the nucleus and the two electrons)?arrow_forwardA hydrogen atom ¹H with 200 eV of kinetic energy has a head-on, perfectly elastic collision with a ¹2C atom at rest. Part A Afterward, what is the kinetic energy, in eV, of ¹H? Express your answer in electron volts. KfH = Submit Part B V Kfc = ΑΣΦ Request Answer Afterward, what is the kinetic energy, in eV, of ¹2C? Express your answer in electron volts. ww ΑΣΦ ? ? eV eVarrow_forward
- Harmonic 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_forwardExplicitly calculate the inner product between P(x) = x, and P,(x) = (63r -70r +15x), and show that it is zero.arrow_forwardCalculate Z for a single oscillator in an Einstein solid at a temperature T=4TE=4ϵ/kBT=4 TE=4 ϵ/kB . The value of Z isarrow_forward
- An a particle passes rapidly through the exact centre of a hydrogen molecule, moving on a line perpendiaular to the internuclear axis. The distance between the nuclei is b. Where on its path does the a particle experience the greatest force? Assume that the nuclei do not move much during the passage of the a particle. Also neglect the electric field of the clectrons in the molecúle. b (a) 2 (b) 2/2 2/2 +2e b a particle (c) J2 (d) none H, - moleculesarrow_forwardb) Find E at (0,4,0) P, = 2 mC 2 (0 4, 0)arrow_forwarda) How many distinct angles from the vertical axis can the orbital angular momentum vector L make for an electron with l = 7? b)Calculate the smallest possible angle the L can make with respect to the vertical axis. (Hint: The smallest angle occurs when ml takes the maximum allowed value. Sketch L in that case and compare the vertical component, which is related to ml, to the magnitude of L, which is related to l.)arrow_forward
- The electron in a hydrogen atom is in the state |v) N[3]W100) + 4 |v211)] where ynlm represents the spatial eigen functions of hydrogen atom. (a) Find N such that the above state normalized. Assume N is real and positive. (b) Is y) an eigen state of the Hamiltonian of hydrogen atom? Justify your answer. (c) Determine expectation value of the Hamiltonian in terms of eigen energies Ei and E2. (d) Determine the expectation values of L, and L?.arrow_forwardA hydrogen atom is in the stationary state (n, I, m) = (5, 3, 1) What is the angle between the angular momentum vector L and Lz? Give you answer to 3 significant figures and in units of degrees, but do not include the units in your answer.arrow_forwardAngular momentum and Spin. An electron in an H-atom has orbital angular momentum magnitude and z-component given by L² = 1(1+1)ħ², L₂ = m₂h, 1 = 0,1,2,..., n-1 m₁ = 0, +1, +2, ..., ±l 3 1 S² = s(s+1)h²=h², S₂ = m₂h = + = h +/-ħ 4 Consider an excited electron (n > 1) on an H-atom. What is the minimum angle 0min that the S can have with the z-axis? Clue: the angle a vector with magnitude V from the z-axis can be computed from cos 0 = V²/Varrow_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 Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning