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1. Sudden switched-on perturbation calculate ca(t) and c,(t) to second order for a two-level syst...
Exercise 8: Time dependence of a two-level system Consider a two-level system with stationary states a and b with unper...
Exercise 8: Time dependence of a two-level system Consider a two-level system with stationary states a and b with unperturbed energies and E() and corresponding eigenfunctions ф ) and 4°, respectively. Assume E ) > E 0. such that the Bohr angular frequency wi(EEis positive. A time-independent perturbation V is switched on at time t 0 a) Write down the coupled set of equations for the coefficients ca(t) and c(t) of the wave function of the system: Note that we...
Please solve the problem as soon as possible. Problem 1: Consider a two level system with Hamiltonian: Using the first order time-dependent perturbation theory, obtain the probability coefficients cn...
Please solve the problem as soon as possible.
Problem 1: Consider a two level system with Hamiltonian: Using the first order time-dependent perturbation theory, obtain the probability coefficients cn (t) if the perturbation is applied at t >0 and the system is originally in the ground state. Hint: When solving the problem, first you may need to find the energies and wave functions of the unperturbed Hamiltonian A0.
Problem 1: Consider a two level system with Hamiltonian: Using the first...
1. The angular displacement e(t) of an undamped pendulum of length l swinging in a vertical...
1. The angular displacement e(t) of an undamped pendulum of length l swinging in a vertical plane under the influence of gravity can be modelled with the nonlinear second order ODE 0"(t) + "$(0(e) – Pef) = = 0, (1) where w2 = { (a) Re-write equation (1) as a system of first-order ODEs by defining (1 = 0(t) and 02 = 't). (b) Find the nullclines and equilibrium points for the system of first-order ODEs. (c) The first order...
Problem 4 (Analytical and Computational-20 points) Given a second-order ordinary differential equation: d2f(t) df(t) with the following initial conditions: (O) 1 and ait 0 (Analytical-10 points)...
Problem 4 (Analytical and Computational-20 points) Given a second-order ordinary differential equation: d2f(t) df(t) with the following initial conditions: (O) 1 and ait 0 (Analytical-10 points) Express Equation (1) in state-space form. Cleary write down the A, B, C, and D matrices. Then find the state transition matrix and determine the solution for f(t) if the input function r(t) is a unit step function. a) b) (Computational-10 points) Write a MATLAB-Simulink program to find the computational solution for f(t) in...
) Solve the nonhomogeneous system: (t) 5 -2 x(sinh(t) 7.jk(t)-| cosh(t)) 20 An interesting applic...
Please show all work for Number 2. Thank you.
) Solve the nonhomogeneous system: (t) 5 -2 x(sinh(t) 7.jk(t)-| cosh(t)) 20 An interesting application that leads to a system of differential equations is the study of an arms race. The presentation given here is often called the Richardson model, since it was first proposed by the English metcorologist L.E Richardson. We wish to consider the problem of two countries with expenditures for armaments, x and y, measured in billions of...
choosing C to make P(t) match P(0) at t = 0. Compute the maximum error over 0 ≤ t ≤ 1 for each solution you obtain. How do the errors change with h for the two methods? dP aP (PM-P). With a 1 and...
choosing C to make P(t) match P(0) at t = 0. Compute the
maximum error
over 0 ≤ t ≤ 1 for each solution you obtain. How do the errors
change with
h for the two methods?
dP aP (PM-P). With a 1 and PM 10, solve this equation with both Euler's method and Heun's method for step sizes h = 10-k for k = 1, 2, 3 for the interval 0 t1. Use the initial value P(O) 1. Given...
EECE 4694 Numerical Methods and Computer Applications Homework -5 1. A condenser of capacity C is...
Please use Matlab to solve this problem
EECE 4694 Numerical Methods and Computer Applications Homework -5 1. A condenser of capacity C is discharged through an inductance L and a resistance R in series, and the chargc g at any timc t is given by at2 Given that L-10mH. R-200 ohms. C-0.1μF, and also when 1-0, charge q- 0.01coulomb, and current 0 i. Using finite difference methods for initial value problems, find the value of q from time t0 to...
Please show all work for Number 2. Thank you. ) Solve the nonhomogeneous system: (t) 5...
Please show all work for Number 2. Thank you.
) Solve the nonhomogeneous system: (t) 5 -2 x(sinh(t) 7.jk(t)-| cosh(t)) 20 An interesting application that leads to a system of differential equations is the study of an arms race. The presentation given here is often called the Richardson model, since it was first proposed by the English metcorologist L.E Richardson. We wish to consider the problem of two countries with expenditures for armaments, x and y, measured in billions of...
1) T/F In order to amplify a gene by PCR, one needs to know the exact...
1) T/F In order to amplify a gene by PCR, one needs to know the exact DNA sequence of the regions flanking the gene. 2) T/F The initiation complex for translation includes transfer RNA-MET. 3) T/F A mutation that changes the amino acid sequence in a protein sometimes increases the fitness of the individual. 4) T/F A mutation in the TATA box will change the level of gene expression. 5) T/F Pyrimidine dimer formation is a common cause of DNA...
(7 10 Two connected tanks, each with a capacity of 60 liters, contain brine (salt water) Initially the firs tank contains 40 liters and the second tank contains 30 liers. Brine with a salt conccntrat...
(7 10 Two connected tanks, each with a capacity of 60 liters, contain brine (salt water) Initially the firs tank contains 40 liters and the second tank contains 30 liers. Brine with a salt conccntration of 1 grams per litcr flows into the first tank at S litcrs per hour. Well-stirred brine flows from the first tank into the second at 7 liters per hour from the second nto the fist at3 lters per honr, from the first into a...
Exercise 8: Time dependence of a two-level system Consider a two-level system with stationary states a and b with unperturbed energies and E() and corresponding eigenfunctions ф ) and 4°, respectively. Assume E ) > E 0. such that the Bohr angular frequency wi(EEis positive. A time-independent perturbation V is switched on at time t 0 a) Write down the coupled set of equations for the coefficients ca(t) and c(t) of the wave function of the system: Note that we...
Please solve the problem as soon as possible.
Problem 1: Consider a two level system with Hamiltonian: Using the first order time-dependent perturbation theory, obtain the probability coefficients cn (t) if the perturbation is applied at t >0 and the system is originally in the ground state. Hint: When solving the problem, first you may need to find the energies and wave functions of the unperturbed Hamiltonian A0.
Problem 1: Consider a two level system with Hamiltonian: Using the first...
1. The angular displacement e(t) of an undamped pendulum of length l swinging in a vertical plane under the influence of gravity can be modelled with the nonlinear second order ODE 0"(t) + "$(0(e) – Pef) = = 0, (1) where w2 = { (a) Re-write equation (1) as a system of first-order ODEs by defining (1 = 0(t) and 02 = 't). (b) Find the nullclines and equilibrium points for the system of first-order ODEs. (c) The first order...
Problem 4 (Analytical and Computational-20 points) Given a second-order ordinary differential equation: d2f(t) df(t) with the following initial conditions: (O) 1 and ait 0 (Analytical-10 points) Express Equation (1) in state-space form. Cleary write down the A, B, C, and D matrices. Then find the state transition matrix and determine the solution for f(t) if the input function r(t) is a unit step function. a) b) (Computational-10 points) Write a MATLAB-Simulink program to find the computational solution for f(t) in...
Please show all work for Number 2. Thank you.
) Solve the nonhomogeneous system: (t) 5 -2 x(sinh(t) 7.jk(t)-| cosh(t)) 20 An interesting application that leads to a system of differential equations is the study of an arms race. The presentation given here is often called the Richardson model, since it was first proposed by the English metcorologist L.E Richardson. We wish to consider the problem of two countries with expenditures for armaments, x and y, measured in billions of...
choosing C to make P(t) match P(0) at t = 0. Compute the
maximum error
over 0 ≤ t ≤ 1 for each solution you obtain. How do the errors
change with
h for the two methods?
dP aP (PM-P). With a 1 and PM 10, solve this equation with both Euler's method and Heun's method for step sizes h = 10-k for k = 1, 2, 3 for the interval 0 t1. Use the initial value P(O) 1. Given...
Please use Matlab to solve this problem
EECE 4694 Numerical Methods and Computer Applications Homework -5 1. A condenser of capacity C is discharged through an inductance L and a resistance R in series, and the chargc g at any timc t is given by at2 Given that L-10mH. R-200 ohms. C-0.1μF, and also when 1-0, charge q- 0.01coulomb, and current 0 i. Using finite difference methods for initial value problems, find the value of q from time t0 to...
Please show all work for Number 2. Thank you.
) Solve the nonhomogeneous system: (t) 5 -2 x(sinh(t) 7.jk(t)-| cosh(t)) 20 An interesting application that leads to a system of differential equations is the study of an arms race. The presentation given here is often called the Richardson model, since it was first proposed by the English metcorologist L.E Richardson. We wish to consider the problem of two countries with expenditures for armaments, x and y, measured in billions of...
(7 10 Two connected tanks, each with a capacity of 60 liters, contain brine (salt water) Initially the firs tank contains 40 liters and the second tank contains 30 liers. Brine with a salt conccntration of 1 grams per litcr flows into the first tank at S litcrs per hour. Well-stirred brine flows from the first tank into the second at 7 liters per hour from the second nto the fist at3 lters per honr, from the first into a...
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