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(3) Take the case of 3 states ji> i-1,2, 3 which are eigenfunctions of H with...
(3)Consider an atomic p-electron (-1) which is governed by the Hamiltonian H-Ho +Hl,where Ho=a L,.bhand H,-./2...
(3)Consider an atomic p-electron (-1) which is governed by the Hamiltonian H-Ho +Hl,where Ho=a L,.bhand H,-./2 where a,bandcare nonzero real numbers with a 굶b. (a) Determine the Hamiltonian in Matrix form for a basis | I,m > with 1-land ,n = 0,±1. You may use the formula (b)Treat H,as a perturbation of Ho. What are the energy eigenvalues and eigenfunctions of the unperturbed problem? (c)Assume as>lcl and bsslcl. Use perturbation theory to calculate eigenvalues of H to first non trivial...
3. Consider a system whose Hamiltonian H, admits two eigenstates y, (with eigenvalues F) and v,...
3. Consider a system whose Hamiltonian H, admits two eigenstates y, (with eigenvalues F) and v, (with eigenvalues E,). Assume E, E, and they are () orthogonal, (ifi) normalized and (ii) non-degenerate. After the perturbation is on the diagonal matrix elements become zero ie, <4, l H'l Ψ)-(4, I H'ly,)-0, while the off diagonal equals to a constant value ie. (v, l H'l%)-(wil H'ly)-c Using the 2nd order perturbation theory evaluate the energy of the perturbed system.
4 A nonlinear oscillator Consider a perturbed harmonic oscillator. Using x p2 H + ke? 2...
4 A nonlinear oscillator Consider a perturbed harmonic oscillator. Using x p2 H + ke? 2 + ex4 2m 1. write this Hamiltonian in terms of â and at 2. At what frequency or frequencies could this system absorb radiation if € = 0, i.e. the oscillator is unperturbed 1 3. Qualitatively, what do the states look like for the perturbed Hamiltonian? Write the new states as a sum of the unperturbed states, without worrying too much about the amplitude...
4. (30 points) Harmonic oscillator with perturbation Recall the Hamiltonian of an harmonic oscillator in 1D:...
4. (30 points) Harmonic oscillator with perturbation Recall the Hamiltonian of an harmonic oscillator in 1D: p21 ÃO = + mwf?, where m is the mass of the particle and w is the angular frequency. Now, let us perturb the oscillator with a quadratic potential. The perturbation is given by Î' = zgmw?h?, where g is a dimensionless constant and g <1. (a) Write down the eigen-energies of the unperturbed Hamiltonian. (b) In Lecture 3, we introduced the lowering (or...
I want a solution to the whole matrix, not just the diagonal, in detail until I...
I want a solution to the whole matrix, not just the diagonal,
in detail until I reach the final solution!
In the discussion of the intermediate Zeeman effect, you learned that both the Zeeman effect and the fine structure effect must be treated on an equal footing. That is, one forms the Hamiltonian matrix of i' = H + Hy then diagonalises it to obtain the perturbed energy states. As an example, we looked into the n = 2 states...
Discretization, ODE solving, condition number. Consider the differential equation 5y"(x) - 2y'(x) +10y(x)0 on the interval x E [0,10] with boundary conditions y(0)2 and y (10) 3 we set up a f...
Discretization, ODE solving, condition number. Consider the differential equation 5y"(x) - 2y'(x) +10y(x)0 on the interval x E [0,10] with boundary conditions y(0)2 and y (10) 3 we set up a finite difference scheme as follows. Divide [0,10] into N-10 sub-intervals, i.e. {xo, X1, [0,1,. 10. Denote xi Xo + ih (here, h- 1) and yi E y(x). Approximate the derivatives as follows X10- 2h we have the following equations representing the ODE at each point Xi ,i = 1,...
2. Consider a mass m moving in R3 without friction. It is fasten tightly at one...
2. Consider a mass m moving in R3 without friction. It is fasten tightly at one end of a string with length 1 and can swing in any direction. In fact, it moves on a sphere, a subspace of R3 1 0 φ g 2.1 Use the spherical coordinates (1,0,) to derive the Lagrangian L(0,0,0,0) = T-U, namely the difference of kinetic energy T and potential energy U. (Note r = 1 is fixed.) 2.2 Calculate the Euler-Lagrange equations, namely...
g) Which structure is Z-2-bromo-3-methyl-2-pentene? CH3 H3C CH2CH3 H C=C CH-CH,CH, CH3 CH3 Вісн. C=C CH3...
g) Which structure is Z-2-bromo-3-methyl-2-pentene? CH3 H3C CH2CH3 H C=C CH-CH,CH, CH3 CH3 Вісн. C=C CH3 Br н Br | BÁ CHẠCH, C=C CH, CHỊCH, 10) Which compounds contain stereocenters? D) 1-chloropentane II) 2-chloropentane III) 3-chloropentane IV) 1,2-dichloropentane 11) Aspartame is an artificial, non-saccharide sweetener. It is made from two amino acids phenylalanine (methyl ester) and aspartic acid. Both aminoacids have one stercocenter. Both stereocenters have S-stereoconfiguration. Which of the two structures is aspartame? H2N-C-C-N-C-0-0 CH2 CH2 c=0 HO HO...
For this project, each part will be in its oun matlab script. You will be uploading a total 3 m f...
For this project, each part will be in its oun matlab script. You will be uploading a total 3 m files. Be sure to make your variable names descriptive, and add comments regularly to describe what your code is doing and hou your code aligns with the assignment 1 Iterative Methods: Conjugate Gradient In most software applications, row reduction is rarely used to solve a linear system Ar-b instead, an iterative algorithm like the one presented below is used. 1.1...
my chemistry lab did the composition of hydrogen peroxide. i am having trouble trying to fugure...
my chemistry lab did the composition of hydrogen peroxide. i
am having trouble trying to fugure out how to fill in the table. i
dont understand why “s” is added to pvnrt and how to apply that to
my equation. these are the steps on how to solve but i believe they
are rather confusing. please help! thank you!
i
dont know how to convert PV=nRT so m/s for the initial rate. im
confused on how to fill out the...
(3)Consider an atomic p-electron (-1) which is governed by the Hamiltonian H-Ho +Hl,where Ho=a L,.bhand H,-./2 where a,bandcare nonzero real numbers with a 굶b. (a) Determine the Hamiltonian in Matrix form for a basis | I,m > with 1-land ,n = 0,±1. You may use the formula (b)Treat H,as a perturbation of Ho. What are the energy eigenvalues and eigenfunctions of the unperturbed problem? (c)Assume as>lcl and bsslcl. Use perturbation theory to calculate eigenvalues of H to first non trivial...
3. Consider a system whose Hamiltonian H, admits two eigenstates y, (with eigenvalues F) and v, (with eigenvalues E,). Assume E, E, and they are () orthogonal, (ifi) normalized and (ii) non-degenerate. After the perturbation is on the diagonal matrix elements become zero ie, <4, l H'l Ψ)-(4, I H'ly,)-0, while the off diagonal equals to a constant value ie. (v, l H'l%)-(wil H'ly)-c Using the 2nd order perturbation theory evaluate the energy of the perturbed system.
4 A nonlinear oscillator Consider a perturbed harmonic oscillator. Using x p2 H + ke? 2 + ex4 2m 1. write this Hamiltonian in terms of â and at 2. At what frequency or frequencies could this system absorb radiation if € = 0, i.e. the oscillator is unperturbed 1 3. Qualitatively, what do the states look like for the perturbed Hamiltonian? Write the new states as a sum of the unperturbed states, without worrying too much about the amplitude...
4. (30 points) Harmonic oscillator with perturbation Recall the Hamiltonian of an harmonic oscillator in 1D: p21 ÃO = + mwf?, where m is the mass of the particle and w is the angular frequency. Now, let us perturb the oscillator with a quadratic potential. The perturbation is given by Î' = zgmw?h?, where g is a dimensionless constant and g <1. (a) Write down the eigen-energies of the unperturbed Hamiltonian. (b) In Lecture 3, we introduced the lowering (or...
I want a solution to the whole matrix, not just the diagonal,
in detail until I reach the final solution!
In the discussion of the intermediate Zeeman effect, you learned that both the Zeeman effect and the fine structure effect must be treated on an equal footing. That is, one forms the Hamiltonian matrix of i' = H + Hy then diagonalises it to obtain the perturbed energy states. As an example, we looked into the n = 2 states...
Discretization, ODE solving, condition number. Consider the differential equation 5y"(x) - 2y'(x) +10y(x)0 on the interval x E [0,10] with boundary conditions y(0)2 and y (10) 3 we set up a finite difference scheme as follows. Divide [0,10] into N-10 sub-intervals, i.e. {xo, X1, [0,1,. 10. Denote xi Xo + ih (here, h- 1) and yi E y(x). Approximate the derivatives as follows X10- 2h we have the following equations representing the ODE at each point Xi ,i = 1,...
2. Consider a mass m moving in R3 without friction. It is fasten tightly at one end of a string with length 1 and can swing in any direction. In fact, it moves on a sphere, a subspace of R3 1 0 φ g 2.1 Use the spherical coordinates (1,0,) to derive the Lagrangian L(0,0,0,0) = T-U, namely the difference of kinetic energy T and potential energy U. (Note r = 1 is fixed.) 2.2 Calculate the Euler-Lagrange equations, namely...
g) Which structure is Z-2-bromo-3-methyl-2-pentene? CH3 H3C CH2CH3 H C=C CH-CH,CH, CH3 CH3 Вісн. C=C CH3 Br н Br | BÁ CHẠCH, C=C CH, CHỊCH, 10) Which compounds contain stereocenters? D) 1-chloropentane II) 2-chloropentane III) 3-chloropentane IV) 1,2-dichloropentane 11) Aspartame is an artificial, non-saccharide sweetener. It is made from two amino acids phenylalanine (methyl ester) and aspartic acid. Both aminoacids have one stercocenter. Both stereocenters have S-stereoconfiguration. Which of the two structures is aspartame? H2N-C-C-N-C-0-0 CH2 CH2 c=0 HO HO...
For this project, each part will be in its oun matlab script. You will be uploading a total 3 m files. Be sure to make your variable names descriptive, and add comments regularly to describe what your code is doing and hou your code aligns with the assignment 1 Iterative Methods: Conjugate Gradient In most software applications, row reduction is rarely used to solve a linear system Ar-b instead, an iterative algorithm like the one presented below is used. 1.1...
my chemistry lab did the composition of hydrogen peroxide. i
am having trouble trying to fugure out how to fill in the table. i
dont understand why “s” is added to pvnrt and how to apply that to
my equation. these are the steps on how to solve but i believe they
are rather confusing. please help! thank you!
i
dont know how to convert PV=nRT so m/s for the initial rate. im
confused on how to fill out the...
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