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Consider the excited state wave function for He atom given by the following Slater determinant 1...
Use the Slater determinant formalism to write the spin-orbital for the ground state of He atom....
Use the Slater determinant formalism to write the spin-orbital for the ground state of He atom. Prove that the wave function that is obtained for this satisfies the anti-symmetric requirements for fermions.
For the Li atom ground state (configuration (1s) (2s)'1, for the z-component of the total spin...
For the Li atom ground state (configuration (1s) (2s)'1, for the z-component of the total spin angular momentumt STo-S +S? +S), determine whether the Slater determinant is an eigenfunction of STod. What is the eigenvalue?
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...
5. Part 1. (6 pt) An electron moves around a 2D ring with ring radius 0.50 nm in the state m --20...
5. Part 1. (6 pt) An electron moves around a 2D ring with ring radius 0.50 nm in the state m --20. Determine the wavelength (in nm) of the particle wave induced by this electron. (similar to a question in Exam 1) Part 2. (a) (7pt) A wavefunction is given by y, (e, 4-B sin cos(6). Can this function be an eigenfunction of Legendrían operator (A2.sunagatsineaesin暘for a quantum particle moving around a spherical surface)? If so, determine the eigenvalue and...
1. Given a state y(r) expanded on the eigenstates of the Hamiltonian for the electron, H, in a hydrogen atom: where the...
1. Given a state y(r) expanded on the eigenstates of the Hamiltonian for the electron, H, in a hydrogen atom: where the subscript of E is n, the principal quantum number. The other two numbers are the 1 and m values, find the expectation values of H (you may use the eigenvalue equation to evaluate for H), L-(total angular momentum operator square), Lz (the z-component of the angular momentum operator) and P (parity operator). Draw schematic pictures of 1 and...
The function ψ2px-1(ψ2,1,1+ψ2,1-1) describes an electron in the 2px state of a hydrogen-like atom (with unspecified...
The function ψ2px-1(ψ2,1,1+ψ2,1-1) describes an electron in the 2px state of a hydrogen-like atom (with unspecified spin). Functions ψη..my are normalized egenfuntions of the energy operator (A), the square of angular momentum operator (12), and the z-component of angular momentum operator (Lz), that is 4. E1 a) Show that the function ψ2px is an eigen function of both the energy operator and the square of angular momentum operator. Find the corresponding eigenvalues. b) Determine the expected value and the uncertainty...
The radial wave function for a hydrogen atom in the 3d state is given by
(25 marks) The radial wave function for a hydrogen atom in the \(3 d\) state is given by \(R(r)=A r^{2} e^{-\alpha r}\), where \(A\) and \(\alpha\) are constants. (a) Determine the constant \(\alpha .[\) Hint \(:\) Consider the radial equation given in the lecture note Ch. 9 page 3\(]\) (b) Determine the largest and smallest possible values of the combination \(\sqrt{L_{x}^{2}+L_{y}^{2}}\) for the \(3 d\) state, where \(L_{x}\) and \(L_{y}\) are the \(x\) - and \(y\) -component of the orbital...
The ground state wave function of the hydrogen atom is given by 1 (r) = 7/a....
The ground state wave function of the hydrogen atom is given by 1 (r) = 7/a. Vπα3 What is the ground state wave function of the hydrogen atom in momentum space? Hint: Choose the z-axis along the momentum direction.
Consider an electron in the state n=4, l=3, m=2, s=1/2. Part A: In what shell is...
Consider an electron in the state n=4, l=3, m=2, s=1/2. Part A: In what shell is this electron located? Part B:In what subshell is this electron located? Part C: How many other electrons could occupy the same subshell as this electron? Part D: What is the orbital angular momentum L of this electron? Part E: What is the z component of the orbital angular momentum of this electron, Lz? Part F: What is the z component of the spin angular...
322 CHAPTER 5. ANGULAR MOMENTUM Problem 5.12 Consider a particle whose wave function is 1 222-x2-y2...
322 CHAPTER 5. ANGULAR MOMENTUM Problem 5.12 Consider a particle whose wave function is 1 222-x2-y2 4 A 3 xz (x, y, z) = 2 2 Calculate L2 (x, y, z) and L-y(x, y, z). Find the total angular momentum of this particle. (b) Calculate L+ y (x, y, z) and (Y L+ W). (c)If a measurement of the z-component of the orbital angular momentum is carried out, find the probabilities corresponding to finding the results 0, h, and -h....
For the Li atom ground state (configuration (1s) (2s)'1, for the z-component of the total spin angular momentumt STo-S +S? +S), determine whether the Slater determinant is an eigenfunction of STod. What is the eigenvalue?
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...
5. Part 1. (6 pt) An electron moves around a 2D ring with ring radius 0.50 nm in the state m --20. Determine the wavelength (in nm) of the particle wave induced by this electron. (similar to a question in Exam 1) Part 2. (a) (7pt) A wavefunction is given by y, (e, 4-B sin cos(6). Can this function be an eigenfunction of Legendrían operator (A2.sunagatsineaesin暘for a quantum particle moving around a spherical surface)? If so, determine the eigenvalue and...
1. Given a state y(r) expanded on the eigenstates of the Hamiltonian for the electron, H, in a hydrogen atom: where the subscript of E is n, the principal quantum number. The other two numbers are the 1 and m values, find the expectation values of H (you may use the eigenvalue equation to evaluate for H), L-(total angular momentum operator square), Lz (the z-component of the angular momentum operator) and P (parity operator). Draw schematic pictures of 1 and...
The function ψ2px-1(ψ2,1,1+ψ2,1-1) describes an electron in the 2px state of a hydrogen-like atom (with unspecified spin). Functions ψη..my are normalized egenfuntions of the energy operator (A), the square of angular momentum operator (12), and the z-component of angular momentum operator (Lz), that is 4. E1 a) Show that the function ψ2px is an eigen function of both the energy operator and the square of angular momentum operator. Find the corresponding eigenvalues. b) Determine the expected value and the uncertainty...
The ground state wave function of the hydrogen atom is given by 1 (r) = 7/a. Vπα3 What is the ground state wave function of the hydrogen atom in momentum space? Hint: Choose the z-axis along the momentum direction.
322 CHAPTER 5. ANGULAR MOMENTUM Problem 5.12 Consider a particle whose wave function is 1 222-x2-y2 4 A 3 xz (x, y, z) = 2 2 Calculate L2 (x, y, z) and L-y(x, y, z). Find the total angular momentum of this particle. (b) Calculate L+ y (x, y, z) and (Y L+ W). (c)If a measurement of the z-component of the orbital angular momentum is carried out, find the probabilities corresponding to finding the results 0, h, and -h....
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