Homework Answers
Add Answer to:
Show that the Slater determinate, including spin, for the helium atom is equal to where φ(1)...
Exercise 1: The helium atom and spin operators 26 pts (a) Show that the expectation value...
Exercise 1: The helium atom and spin operators 26 pts (a) Show that the expectation value of the Hamiltonian in the (sa)'(2a)' excited state of helium is given by E = $42.0) (Avo ) anordes ++f63,(-) (%13-12 r) 62(e)drz + løn.(r.) per 142, (ra)]" drų dr2 - / 01.(ru) . (ra) Anemia 02.(r.)61.(r.)dr; dr2 (1) Use the approximate, antisymmetrized triplet state wave function for the (Isa)'(280)' state as discussed in class. Hint: make use of the orthonormality of the hydrogenic...
(L43*) Spin can be represented by matrices. Show that all three spin matrices l 0 2 0 -1 0),"2=2 1 have eigenval...
(L43*) Spin can be represented by matrices. Show that all three spin matrices l 0 2 0 -1 0),"2=2 1 have eigenvalues of +1/2h and -1/2h. Calculate the corresponding eigenfunctions which we will denote as α-and β-eigenfunctions corresponding to spin l/2 particles. Show that Sj can be determined by the commutation of the other two matrices sn and sm, n, maj. Prove that the (2×2) matrix sz-s' +ss+s, commutes with all spin matrices, ie. s2s,-sis-. Calculate the eigenvalues of s2....
4. (20 points). Consider a deuterium atom (composed of a nucleus with spin I - 1...
4. (20 points). Consider a deuterium atom (composed of a nucleus with spin I - 1 and an electron) The electronic angular momentum is J- L S, where L is the orbital angular momentum of the electron and S is its spin. The total angular momentum of the atom is F-J+I. The eigenvalues of J2 and F2 are j(j + 1)n° and f(f+1)ћ, respectively a. What are the possible values of the quantum numbers j and f for a deuterium...
Consider the excited state wave function for He atom given by the following Slater determinant 1...
Consider the excited state wave function for He atom given by the following Slater determinant 1 432,0(1) V3.2,-2B(1) He (1,2)= V2 V3.2,a(2) W32,-2B(2) Here Y 3,2,-and Y3,2,-2 are hydrogenic wave functions (with Z = 2, see the equation sheet). Show that He (1, 2) is an eigenfunction of Î. = Î., +Î.2. What is the eigenvalue? Î.,, ..2, and Î, are the z-components of the orbital angular momentum operators for electrons 1 and 2, and the z-component of the total...
2. Spin-1/2 system: (20 points) The Pauli matrices are, 0 -1 from which we can define...
2. Spin-1/2 system: (20 points) The Pauli matrices are, 0 -1 from which we can define the spin matrices, s.-슬&z, Šv = , S.-출.. We'll use the eigenkets of S that, for the spin half system, they can be represented by the spinors, a) Show, by matrix multiplication that |+) and |-) are eigenstates of the S operator and determine the eigenvalues. Show that they are not eigenstates of S and Sy b) Show that the matrix squares s ,...
Problem 2. (30 points) The spin states: s 1,m) and Is -2, m1) composed of spin-3/2 and spin-1/2 states are linear combi...
Problem 2. (30 points) The spin states: s 1,m) and Is -2, m1) composed of spin-3/2 and spin-1/2 states are linear combinations of s1 3/2,m-3/2;2 1/2,m2 1/2) and 81-3/2, m-1/2; 2 1/2, m2--1/2), that is 11.-1)-cos θ3/2,-3/2; 1/2, 1/2) _ sin θ|3/2.-1/2; 1/2,-1/2), 2.-1) sin θ|3/2,-3/2; 1/2, 1/2) + cos θ|3/2.-1/2: 1/2,-1/2) a) Determine the values for cos θ and sin θ b) Express |3/2,-3/2; 1/2, 1/2) and |3/2,-1/2;1/2,-1/2) as functions of |1, -1) and 2,-1) c) A system of...
3. The predecessor to Hartree-Fock was the Hartree method, where the main difference is that the ...
Questions 3-5
3. The predecessor to Hartree-Fock was the Hartree method, where the main difference is that the Hartree-Fock method includes an trial wavefunction by writing it as a Slater Determinant, while the Hartree method uses a simple product wavefunction that does not capture anti- symmetry. In particular, for a minimal-basis model of, the Hartree method's trial wavefunction is given in the while the Hartree-Fock trial wav is given by where and are molecular orbitals, and and coordinates of electron...
Given the production function: y=Alα, where l=labor and 0<α<1, price and wage are equal to P...
Given the production function: y=Alα, where l=labor and 0<α<1, price and wage are equal to P and W, respectively. a) Find the profit-maximizing level of labor. b) Show that the SOC is satisfied. c) Show that demand for labor is inversely related to W and directly related to P. No need to take derivatives.
N(4il+), +31-)). 1. Calculate the inner product z(+lk). Clearly show each step in your calculation, including...
N(4il+), +31-)). 1. Calculate the inner product z(+lk). Clearly show each step in your calculation, including C. Consider the same state vector Ix)- any use of orthonormality. 2. Suppose this electron is sent through a Stern-Gerlach apparatus. Determine the probability that spin up in the z-direction would be measured in terms of N. Show your work. Determine the probability that spin down in the z-direction would be measured in terms of N. Show your work. 3. Determine the constant N....
Exercise 1: The helium atom and spin operators 26 pts (a) Show that the expectation value of the Hamiltonian in the (sa)'(2a)' excited state of helium is given by E = $42.0) (Avo ) anordes ++f63,(-) (%13-12 r) 62(e)drz + løn.(r.) per 142, (ra)]" drų dr2 - / 01.(ru) . (ra) Anemia 02.(r.)61.(r.)dr; dr2 (1) Use the approximate, antisymmetrized triplet state wave function for the (Isa)'(280)' state as discussed in class. Hint: make use of the orthonormality of the hydrogenic...
(L43*) Spin can be represented by matrices. Show that all three spin matrices l 0 2 0 -1 0),"2=2 1 have eigenvalues of +1/2h and -1/2h. Calculate the corresponding eigenfunctions which we will denote as α-and β-eigenfunctions corresponding to spin l/2 particles. Show that Sj can be determined by the commutation of the other two matrices sn and sm, n, maj. Prove that the (2×2) matrix sz-s' +ss+s, commutes with all spin matrices, ie. s2s,-sis-. Calculate the eigenvalues of s2....
4. (20 points). Consider a deuterium atom (composed of a nucleus with spin I - 1 and an electron) The electronic angular momentum is J- L S, where L is the orbital angular momentum of the electron and S is its spin. The total angular momentum of the atom is F-J+I. The eigenvalues of J2 and F2 are j(j + 1)n° and f(f+1)ћ, respectively a. What are the possible values of the quantum numbers j and f for a deuterium...
Consider the excited state wave function for He atom given by the following Slater determinant 1 432,0(1) V3.2,-2B(1) He (1,2)= V2 V3.2,a(2) W32,-2B(2) Here Y 3,2,-and Y3,2,-2 are hydrogenic wave functions (with Z = 2, see the equation sheet). Show that He (1, 2) is an eigenfunction of Î. = Î., +Î.2. What is the eigenvalue? Î.,, ..2, and Î, are the z-components of the orbital angular momentum operators for electrons 1 and 2, and the z-component of the total...
2. Spin-1/2 system: (20 points) The Pauli matrices are, 0 -1 from which we can define the spin matrices, s.-슬&z, Šv = , S.-출.. We'll use the eigenkets of S that, for the spin half system, they can be represented by the spinors, a) Show, by matrix multiplication that |+) and |-) are eigenstates of the S operator and determine the eigenvalues. Show that they are not eigenstates of S and Sy b) Show that the matrix squares s ,...
Problem 2. (30 points) The spin states: s 1,m) and Is -2, m1) composed of spin-3/2 and spin-1/2 states are linear combinations of s1 3/2,m-3/2;2 1/2,m2 1/2) and 81-3/2, m-1/2; 2 1/2, m2--1/2), that is 11.-1)-cos θ3/2,-3/2; 1/2, 1/2) _ sin θ|3/2.-1/2; 1/2,-1/2), 2.-1) sin θ|3/2,-3/2; 1/2, 1/2) + cos θ|3/2.-1/2: 1/2,-1/2) a) Determine the values for cos θ and sin θ b) Express |3/2,-3/2; 1/2, 1/2) and |3/2,-1/2;1/2,-1/2) as functions of |1, -1) and 2,-1) c) A system of...
Questions 3-5
3. The predecessor to Hartree-Fock was the Hartree method, where the main difference is that the Hartree-Fock method includes an trial wavefunction by writing it as a Slater Determinant, while the Hartree method uses a simple product wavefunction that does not capture anti- symmetry. In particular, for a minimal-basis model of, the Hartree method's trial wavefunction is given in the while the Hartree-Fock trial wav is given by where and are molecular orbitals, and and coordinates of electron...
N(4il+), +31-)). 1. Calculate the inner product z(+lk). Clearly show each step in your calculation, including C. Consider the same state vector Ix)- any use of orthonormality. 2. Suppose this electron is sent through a Stern-Gerlach apparatus. Determine the probability that spin up in the z-direction would be measured in terms of N. Show your work. Determine the probability that spin down in the z-direction would be measured in terms of N. Show your work. 3. Determine the constant N....
Most questions answered within 3 hours.
-
Calculate the pH of a 5.7 M solution of aniline (C6H5NH2; Kb =
3.8 x 10^-10)
asked 51 minutes ago -
LSL R3, R3, R12
Memory
Address
Orig.
Data
Updated
Data
Register
Orig.
Data
Updated
Data
0x84F0...
asked 53 minutes ago -
Air at 100 kPa and density of 1.2 kg/m3 flows upward through a
5-cm diameter inclined...
asked 1 hour ago -
Define the following concepts in your own words: (a) stiffness,
(b) strength, (c) strain,
(d) ductility,...
asked 1 hour ago -
In C++
In this homework, you will be tasked with creating functions to
manipulate strings that...
asked 2 hours ago -
An isolated colony represents a pure culture. one rare occasions
, however , a colony can...
asked 2 hours ago -
*****DO NOT ANSWER THIS QUESTION IF YOU DON'T
KNOW*******Rights and Duties of Auditors; Minimum 4000
words...
asked 3 hours ago -
The probability that Janie is wearing sunglasses is 1/4. The
probability that she is wearing sunglasses...
asked 4 hours ago -
Do you believe social media is more of a help or a hindrance in
controlling crises...
asked 4 hours ago -
Two long, parallel wires separated by 2.85 cm carry currents in
opposite directions. The current in...
asked 3 hours ago -
Question # 1. Develop a list of rehabilitation journals
that publish articles concerning career counseling for...
asked 4 hours ago -
Bryant Company has a factory machine with a book value of
$85,100 and a remaining useful...
asked 4 hours ago