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 8.4, Problem 8.12P
To determine
Show that the antisymmetric state can be expressed in terms of molecular orbital’s.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
For Problem 9.18, how do I determine part A & B? This is from a chapter titled, "Electron Spin." This chapter is part of quantum mechanics.
A better description of the molecule in Exercise E9B.1(a) might be obtained by including more orbitals on each atom in the linear combination. Normalize to 1 the molecular orbital ψ = ψA + λψB + λ′ψB′ in terms of the parameters λ and λ′ and the appropriate overlap integrals, where ψB and ψB′ are mutually orthogonal and normalized orbitals on atom B.
For a unit cell with the set of real crystal lattice vectors
a1 = (9.96,0,0)
a2 = (5.58, 12.7,0)
az = (-1.31, -4.33,4.75)
Calculate the dot product of the real and reciprocal lattice vectors:
a1 b2
Report your result to 2 decimal places.
Chapter 8 Solutions
Introduction To Quantum Mechanics
Knowledge Booster
Similar questions
- For a spherical sodium particle of 25 nm radius crystalizing in a BCC structure having a density of 1.51 g/cm^3, estimate the surface energy of the particle. b. Estimate the surface energy of {100},{110} and {111} surfaces of an FCC lattice with bond strength of 7.97 eV and lattice parameter of 4.2 Å. Also compare the energies.arrow_forwardStarting from the N(p) expression of a 3D conductor, derive an expression for the exact density of states D(E) for the 3D conductor in the below graph (You have to show all the steps that lead to your final answer). The length of the conductor is given as L = 20 nm and the diameter is given as D= 4 nm. The +E.. 2mo energy momentum relationship is given as: E =arrow_forwardA conduction electron is confined to a metal wire of length (1.46x10^1) cm. By treating the conduction electron as a particle confined to a one-dimensional box of the same length, find the energy spacing between the ground state and the first excited state. Give your answer in eV. Note: Your answer is assumed to be reduced to the highest power possible. Your Answer: x10 Answerarrow_forward
- The Morse potential The harmonic potential, V(x) = ½kx?, is useful start for modelling molecular vibrations, but it has limitations. A realistic potential between to atoms should accurately represent the sharp increase in the potential as two nuclei come in close proximity, and also have the ability for a bond to break: that is, an asymptote V →0 as x →00. One option, as shown in the figure, is the Morse potential: V(r) = D(1 – e-«(r=re))2 15 10 10 15 20 The parameter D is the well depth (or binding energy) of the potential, re is the bond length, and a is the anharmonicity constant.arrow_forwardExercise 9.4.3. Ignore the fact that the hydrogen atom is a three-dimensional system and pretend that e? H= 2m (R?)/2 (P² = P? + P; + P? , R² = X² + Y² +Z³) corresponds to a one-dimensional problem. Assuming ΔΡ- ΔR> h/2 estimate the ground-state energy.arrow_forwardProblem 4. Consider two indistinguishable, noninteracting spin-1/2 fermions in a one- dimensional infinite square well potential of length L. (a) What is the ground-state energy of the two-particle system? (b) What is the ground-state quantum state vector? (c) What is the first excited state energy of the two-particle system? (d) What are the quantum state vectors of the first excited state? (e) What is the degeneracy of the first excited state? (f) Discuss qualitatively how the excited-state energies change if we consider the particles to be interacting through the Coulomb potential.arrow_forward
- Q.3 a) Which type of molecules exhibit infra-red spectra? Calculate the vibrational energy and force constant of 'H"F if its vibrational frequency is 3.0 x 1014 Hz. b) Prove that the eigenvalues of a Hermitian operator are real.arrow_forward1. According to molecular orbital theory we may construct a ols bonding and antibonding molecular orbital from 1s atomic orbitals on center A and center B of H. (a) Sketch ý and IV? for the bonding and antibonding orbitals A A B Va A A В (b) write the Hamiltonian for this system (easiest in atomic units). FIGURE 9.2 Definition of the distances involved in the Hamiltonian operator for H; (Equation 9.4). (c) Write expressions for the bonding and antibonding energies in terms of the energy of a 1s atomic orbital, the coulombic integral and the exchange integral.arrow_forwardProblem 8.3 Show that the Bose-Hubbard model has the superfluid ground state at integer µ/U for any value of hopping by using the degenerate pertur- bation theory.arrow_forward
- 4. (Kittel 7.4) Chemical potential versus temperature. Explain graphically why the initial curvature of u versus 7 is upward for a fermion gas in one dimension and downward in three dimensions (Figure 7.7). Hint: The D₁(e) and D, (e) curves are different, where D, is given in Problem 1. It will be found useful to set up the integral for N, the number of particles, and to consider from the graphs the behavior of the integrand between zero temperature and a finite temperature.arrow_forward1.7 A crystal has a basis of one atom per lattice point and a set of primitive translation vectors (in A): c = 1.5(i + j+ k), a = 3i, where i, j and k are unit vectors in the x, y and z directions of a Cartesian coordinate system. What is the Bravais lattice type of this crystal, and what are the Miller indices of the set of planes most densely populated with atoms? Calculate the volumes of the primitive unit cell and the conventional unit cell. b= 3j.arrow_forwardQ.4 For a diatomic linear chain, the phonon dispersion relation o(k) has two branches, according to the+ and - sign in the equation below: 0² 1 1 (+) M₁ M₂ =C 1 + M₁ M₂. 2 1/2 ka 쌀² 4 M₁M₂ 2 sin ² There are two atoms in the unit cell with masses M₁ and M₂, and the force constant of the nearest-neighbor interaction is given by c. Show that for M₁ = M2, the result is equivalent to the dispersion curve of the single-atom chain.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
University Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax