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Problem 1. (total: 20 points) Find (r) for all nine (9) of the degenerate n =...
2. The 2p, and 2py wave functions are constructed as linear combinations of the n-2, l-1, m+ 1 wa...
2. The 2p, and 2py wave functions are constructed as linear combinations of the n-2, l-1, m+ 1 wave functions which are eigenfunctions of the hydrogen atom Hamiltonian. Are 2px and 2py wave functions also eigenfunctions of the hydrogen atom Hamiltonian? In other words, do 2px and 2py wave functions denote the same energy states as n=2, 1-1, m=-1 wave functions of the hydrogen atom? (20 points).
2. The 2p, and 2py wave functions are constructed as linear combinations of...
2. The 2p and 2py wave functions are constructed as linear combinations of the n-2, 1-1,...
2. The 2p and 2py wave functions are constructed as linear combinations of the n-2, 1-1, m,- 1 wave functions which are eigenfunctions of the hydrogen atom Hamiltonian. Are 2px and 2py wave functions also eigenfunctions of the hydrogen atom Hamiltonian? In other words, do 2px and 2py wave functions denote the same energy states as n-2, -1, mF+ 1 wave functions of the hydrogen atom? (20 points).
Problem 3 (20 points): An array A of size (n) contains floating-point items. 1. Implement a...
Problem 3 (20 points): An array A of size (n) contains floating-point items. 1. Implement a Divide & Conquer algorithm to return the number of items with values less than a given value (x). (5 points) 2. Test your algorithm by generating an array A of size n = 1024 random floating-point numbers with each number R between 0 and 1, i.e. 0.0 <R< 1.0. Run the algorithm to find the percentage of the numbers in the array with values...
1) (60 points) The ground state of the hydrogen atom: In three dimensions, the radial part...
1) (60 points) The ground state of the hydrogen atom: In three dimensions, the radial part of the Schrodinger equation appropriate for the ground state of the hydrogen atom is given by: ke2 -ħ2 d2 (rR) = E(rR) 2me dr2 where R(r) is a function of r. Here, since we have no angular momentum in the ground state the angular-momentum quantum number /=0. (a) Show that the function R(r) = Ae-Br satisfies the radial Schrodinger equation, and determine the values...
Problem 1. (50 points) a) Using mesh analysis find the matrix R and E of the...
Problem 1. (50 points) a) Using mesh analysis find the matrix R and E of the equation RxI-E b) Find the unknown currents ll, 12, 13, IRI, İR5of the network in mA using mesh analysis. c) Indicate on the circuit IRI, IRs current directions. R, IR E1-3 E2-15; R1-25 R2-8; R3-40 R4-26i R5-22 RS
(20 points) Treat the hydrogen atom as a one-dimensional problem, where the electron is confined to the diameter of the atom in the first excited state (n-2). a.) Use the uncertainty principle to...
(20 points) Treat the hydrogen atom as a one-dimensional problem, where the electron is confined to the diameter of the atom in the first excited state (n-2). a.) Use the uncertainty principle to estimate the minimum kinetic energy of an electron in this state, assuming that the uncertainty in position equal to it's diameter. (Note: Relativistic corrections are not necessary). b.) Assuming this excited electron only remains in this state for 0.1 ns, before emitting a photon and returning to...
Problem #1(20 points) Assuming R1 R2 = R3 = R4 = 10 ohm. Find 1. The...
Problem #1(20 points) Assuming R1 R2 = R3 = R4 = 10 ohm. Find 1. The equivalent resistance of the circuit below. (5 points) 2. Power drawn from the battery (5 points) 3. Voltage drop as seen at terminals a, b (10 points) R3 10 2 R2 RA R1 5Q 25 V b ww
Problem 3. (20 points) Define a relation among the functions that map from N to R+...
Problem 3. (20 points) Define a relation among the functions that map from N to R+ as follows: f(n) g(n) iff f (n) is o(g(n)) i.e. f(n) is O(gfn) but g(n) is not O(f(n)). Order the following functions according to <assuming e is a real constant, 0<E<1. Provide justifcations for your answer. (a) n log n, ( e), and (h) (1/3)" ni+e, (e) (n Problem 4. (15 points) Solve the following recurrence equations and give the solution in θ notation;...
PROBLEM 3. points 30 Use MATL.AB You are given the following cquations of r, y, z as functions of...
PROBLEM 3. points 30 Use MATL.AB You are given the following cquations of r, y, z as functions of the parametcr c 7x +3y-52 13 1. points 5 Use MATLAB's built-in function linsolve under the symbolic mode syms to solve the above system 3. Your solutions will be functions of c. using a for loop programming structure. Take steps of 0.5. plot, for 10 cs 10. Comment on the results. 2. points 20 Solve numerically the system 3 for different...
i=1 For en The purpose of this problem is to show that there exists a set...
i=1 For en The purpose of this problem is to show that there exists a set whose fractal dimension does not exist. Let A be the following subset of [0,1], where we think of representing each point of [0,1] by it's base ten series expansion(s): di A={r=Č : di € {0,1,...,9} 101 and di = 0 whenever there exists n € NU{0} such that 22n <i < 22n+1 – 1}. 10-2", n=0,1,2, ..., show In N (A, €2n) 2 In...
2. The 2p, and 2py wave functions are constructed as linear combinations of the n-2, l-1, m+ 1 wave functions which are eigenfunctions of the hydrogen atom Hamiltonian. Are 2px and 2py wave functions also eigenfunctions of the hydrogen atom Hamiltonian? In other words, do 2px and 2py wave functions denote the same energy states as n=2, 1-1, m=-1 wave functions of the hydrogen atom? (20 points).
2. The 2p, and 2py wave functions are constructed as linear combinations of...
2. The 2p and 2py wave functions are constructed as linear combinations of the n-2, 1-1, m,- 1 wave functions which are eigenfunctions of the hydrogen atom Hamiltonian. Are 2px and 2py wave functions also eigenfunctions of the hydrogen atom Hamiltonian? In other words, do 2px and 2py wave functions denote the same energy states as n-2, -1, mF+ 1 wave functions of the hydrogen atom? (20 points).
Problem 3 (20 points): An array A of size (n) contains floating-point items. 1. Implement a Divide & Conquer algorithm to return the number of items with values less than a given value (x). (5 points) 2. Test your algorithm by generating an array A of size n = 1024 random floating-point numbers with each number R between 0 and 1, i.e. 0.0 <R< 1.0. Run the algorithm to find the percentage of the numbers in the array with values...
1) (60 points) The ground state of the hydrogen atom: In three dimensions, the radial part of the Schrodinger equation appropriate for the ground state of the hydrogen atom is given by: ke2 -ħ2 d2 (rR) = E(rR) 2me dr2 where R(r) is a function of r. Here, since we have no angular momentum in the ground state the angular-momentum quantum number /=0. (a) Show that the function R(r) = Ae-Br satisfies the radial Schrodinger equation, and determine the values...
Problem 1. (50 points) a) Using mesh analysis find the matrix R and E of the equation RxI-E b) Find the unknown currents ll, 12, 13, IRI, İR5of the network in mA using mesh analysis. c) Indicate on the circuit IRI, IRs current directions. R, IR E1-3 E2-15; R1-25 R2-8; R3-40 R4-26i R5-22 RS
(20 points) Treat the hydrogen atom as a one-dimensional problem, where the electron is confined to the diameter of the atom in the first excited state (n-2). a.) Use the uncertainty principle to estimate the minimum kinetic energy of an electron in this state, assuming that the uncertainty in position equal to it's diameter. (Note: Relativistic corrections are not necessary). b.) Assuming this excited electron only remains in this state for 0.1 ns, before emitting a photon and returning to...
Problem #1(20 points) Assuming R1 R2 = R3 = R4 = 10 ohm. Find 1. The equivalent resistance of the circuit below. (5 points) 2. Power drawn from the battery (5 points) 3. Voltage drop as seen at terminals a, b (10 points) R3 10 2 R2 RA R1 5Q 25 V b ww
Problem 3. (20 points) Define a relation among the functions that map from N to R+ as follows: f(n) g(n) iff f (n) is o(g(n)) i.e. f(n) is O(gfn) but g(n) is not O(f(n)). Order the following functions according to <assuming e is a real constant, 0<E<1. Provide justifcations for your answer. (a) n log n, ( e), and (h) (1/3)" ni+e, (e) (n Problem 4. (15 points) Solve the following recurrence equations and give the solution in θ notation;...
PROBLEM 3. points 30 Use MATL.AB You are given the following cquations of r, y, z as functions of the parametcr c 7x +3y-52 13 1. points 5 Use MATLAB's built-in function linsolve under the symbolic mode syms to solve the above system 3. Your solutions will be functions of c. using a for loop programming structure. Take steps of 0.5. plot, for 10 cs 10. Comment on the results. 2. points 20 Solve numerically the system 3 for different...
i=1 For en The purpose of this problem is to show that there exists a set whose fractal dimension does not exist. Let A be the following subset of [0,1], where we think of representing each point of [0,1] by it's base ten series expansion(s): di A={r=Č : di € {0,1,...,9} 101 and di = 0 whenever there exists n € NU{0} such that 22n <i < 22n+1 – 1}. 10-2", n=0,1,2, ..., show In N (A, €2n) 2 In...
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