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
Concept explainers
Question
Chapter 11.3, Problem 11.15P
(a)
To determine
Whether the derivation for the commutation relation
(b)
To determine
The implications obtained by sandwich the commutator,
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
The coordinates of unit a, of the atoms in a body-centered cubic lattice are (0,0,0), (0,1,0), (0,0,1), (0,1,1), (1,0,0), (1,1,0), (1,0,1), (1,1,1) and (1/2;1/2,1/2). Calculate the structure factors Fhkl when all the atoms are identical
Estimate kBT at room temperature, and convert this energy into electronvolts (eV). Using this result, answer the following:
(a) Would you expect hydrogen atoms to be ionized at room temperature? (The binding energy of an electron in a hydrogen atom is 13.6 eV.)
(b) Would you expect the rotational energy levels of diatomic molecules to be excited at room temperature? (It costs about 10-4 eV to promote such a system to an excited rotational energy level.)
4.3 Neon (Ne) is a crystalline solid with an FCC structure. The interatomic energy per atom can be
written as:
20 [(12.13)(=) - (14.45()*] (eV / ate
atom)
U(R)=28
Where & and σ are constants that depend on the polarizability, and mean dipole moment, and
the extent of overlap of core electrons. For crystalline Ne, ε = 3.121 x 103 eV and
o = 0.274 nm.
(a) Show that the equilibrium separation between the atoms in an inert gas crystal is given
by ro= (1.090). What is the equilibrium interatomic separation in the Ne crystal?
(b) Find the bonding energy per atom in solid Ne.
(c) Calculate the density of solid Ne (atomic mass = 20.18 g/mol)
Chapter 11 Solutions
Introduction To Quantum Mechanics
Ch. 11.1 - Prob. 11.1PCh. 11.1 - Prob. 11.2PCh. 11.1 - Prob. 11.3PCh. 11.1 - Prob. 11.4PCh. 11.1 - Prob. 11.5PCh. 11.1 - Prob. 11.6PCh. 11.1 - Prob. 11.7PCh. 11.1 - Prob. 11.8PCh. 11.1 - Prob. 11.9PCh. 11.3 - Prob. 11.10P
Ch. 11.3 - Prob. 11.11PCh. 11.3 - Prob. 11.12PCh. 11.3 - Prob. 11.13PCh. 11.3 - Prob. 11.14PCh. 11.3 - Prob. 11.15PCh. 11.3 - Prob. 11.16PCh. 11.4 - Prob. 11.17PCh. 11.5 - Prob. 11.18PCh. 11.5 - Prob. 11.19PCh. 11.5 - Prob. 11.20PCh. 11.5 - Prob. 11.21PCh. 11.5 - Prob. 11.22PCh. 11 - Prob. 11.23PCh. 11 - Prob. 11.24PCh. 11 - Prob. 11.25PCh. 11 - Prob. 11.26PCh. 11 - Prob. 11.27PCh. 11 - Prob. 11.28PCh. 11 - Prob. 11.29PCh. 11 - Prob. 11.30PCh. 11 - Prob. 11.31PCh. 11 - Prob. 11.33PCh. 11 - Prob. 11.35PCh. 11 - Prob. 11.36PCh. 11 - Prob. 11.37P
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
- Find the angle between these given vectors: u3D{7.19] v- (12,-5]arrow_forward13.43 A one-dimensional harmonic oscillator in the ground state is acted upon by a uniform electric field 6(1) switched on at t = -o. The field is parallel to the axis of the oscillator. (a) What is the probability that the oscillator suffers a transition to its first excited state at t= +0? (b) Show that no other transition is possible.arrow_forwardHcp structure . Show that the c/a ratio for an ideal hexagonal close- packed structure is (8/3)^1/2 = 1.633 . if c/a is significantly larger than this value , the crystal structure may be thought of as composed of planes of closely packed atoms, the planes being loosely stacked.arrow_forward
- A molecule has a C3 axis of rotation and a reflection plane perpendicular to this axis. Suppose that there is at least one other reflection plane (there may be more than one!), but no higher order proper rotation axes present. Determine the following features concerning the symmetry of the molecule. (a) List all the symmetry elements that must be present. (b) What is the order, h, of the point group? (c) How many irreducible representations would you expect to find for this symmetry group?arrow_forward11.15 A cylinder is separated into two compartments by a free sliding piston. Two ideal Fermi gases are placed into the two compartments, numbered 1 and 2. The particles in compartment 1 have spin , while those in compartment 2 have spin . They all have the same mass. Find the equilibrium relative density of the two gases at T = 0 and at T → co.arrow_forwardFind the repulsive exponent n. Given: nearest neighbour equilibrium distance, R0 = 3.14 Å, compressibility of KCl, K = 5.747 x 10–11 m2/N and Madelung constant M = 1.748. please write on a paperarrow_forward
- Find the directional derivative of = 4xz^3 - 3x(^2)y(^2)z at (2,-1,2) in the direction 2i - 3j + 6k . SHOW YOUR SOLUTIONS.arrow_forwardS² = 4f² cos² TC h+2k 3 + Prove that the composition factor of the Zn unit cell of the hexagonal compact structure HCP, which coordinates | The atoms in it are (1/3,2/3,1/2), (0,0,0) given by the relationshiparrow_forwardThe CO molecule, assumed to experience normal vibration mode, is illustrated as follows: k k C X3 Answer the following questions: Calculate analytically the value of w and its eigenvectors.arrow_forward
- Calculate the energy in J, of a CO molecule described by 2,5,3 in a box of dimensions x=10cm, y=10cm, and z=10cm.arrow_forwardFind the repulsive exponent n. Given: nearest neighbour equilibrium distance, R0 = 3.14 Å, compressibility of KCl, K = 5.747 x 10–11 m2/N and Madelung constant M = 1.748arrow_forwardLinear ionic crystal. Consider a line of 2N ions of alternating charge ±q with a repulsive potential energy A/R" between nearest neighbors. (a) Show that at the equilibrium separation 2Nq² In 2/ (CGS) U(R,) = %3D - Ro (b) Let the crystal be compressed so that Ro→ R,(1 – 8). Show that the work done in compressing a unit length of the crystal has the leading term C8², where (CGS) (n – 1)q² In 2 C = Ro To obtain the results in SI, replace q by q*/4TTE9. Note: We should not expect to ob- tain this result from the expression for U(Ro), but we must use the complete expres-arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
University Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Lecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
University Physics (14th Edition)
Physics
ISBN:9780133969290
Author:Hugh D. Young, Roger A. Freedman
Publisher:PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:9781107189638
Author:Griffiths, David J., Schroeter, Darrell F.
Publisher:Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:9780321820464
Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...
Physics
ISBN:9780134609034
Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:PEARSON