Homework Answers
Add Answer to:
5.8 Solve for the eigenfunctions and eigenvalues of the Hamiltonian of the two-dimensional isotropic harmonic oscillator in polar coordinates. Bibliography 5.8 Solve for the eigenfunctions an...
1. The two dimensional Harmonic Oscillator has the Hamiltonian n, n'>denotes the state In> of the...
Please solve with the
explanations of notations
1. The two dimensional Harmonic Oscillator has the Hamiltonian n, n'>denotes the state In> of the x-oscillator and In'> of the y-oscillator. This system is perturbed with the potential energy: Hi-Kix y. The perturbation removes the The perturbation removes the degeneracy of the states | 1,0> and |0,1> a) In first order perturbation theory find the two nondegenerate eigenstates of the full b) Find the corresponding energy eigenvalues. На Hamiltonian as normalized linear...
3. Anharmonicity (6 marks] Consider the three-dimensional isotropic harmonic oscillator 2 1 242 р...
3. Anharmonicity (6 marks] Consider the three-dimensional isotropic harmonic oscillator 2 1 242 рґ which has energy eigenvalues En-hu(n+3/2), where n- 0,1,2.. (a) Calculate the first-order shift in the ground-state energy of the harmonic oscillator due to the addition of an anharmonic term C24 to the potential, where C> 0. (b) Calculate instead the first-order shifts in the energies of the n - 1 ercited states due to the addition of the anharmonic term C (c) For the lowest energy...
Will Rate! Please write clearly, thank you Problem 30: 2D harmonic Oscillator (6 pts Setup the Hamilton-Jacobi Differntial equation in cartesian coordinates for the 2-dimensional harmonic oscillator...
Will Rate!
Please write clearly, thank you
Problem 30: 2D harmonic Oscillator (6 pts Setup the Hamilton-Jacobi Differntial equation in cartesian coordinates for the 2-dimensional harmonic oscillator and solve it. Find x(t) and y(t)
Problem 30: 2D harmonic Oscillator (6 pts Setup the Hamilton-Jacobi Differntial equation in cartesian coordinates for the 2-dimensional harmonic oscillator and solve it. Find x(t) and y(t)
Problem 4.39 Because the two-dimensional harmonic oscillator potential is spherically symmetric, ...
Problem 4.39 Because the two-dimensional harmonic oscillator potential is spherically symmetric, the Schrödinger equation can be handled by separation of variables in spherical coordinates, as well as cartesian coordinates. Use the power series method to solve the radial equation. Find the recursion formula for the coefficients, and determine the allowed energies. Check your answer
Problem 4.39 Because the two-dimensional harmonic oscillator potential is spherically symmetric, the Schrödinger equation can be handled by separation of variables in spherical coordinates, as well...
A particle of mass m is bound by the spherically-symmetric three-dimensional harmonic- oscillator potential energy ,...
A particle of mass m is bound by the spherically-symmetric three-dimensional harmonic- oscillator potential energy , and ф are the usual spherical coordinates. (a) In the form given above, why is it clear that the potential energy function V) is (b) For this problem, it will be more convenient to express this spherically-symmetric where r , spherically symmetric? A brief answer is sufficient. potential energy in Cartesian coordinates x, y, and z as physically the same potential energy as the...
A particle with mass m is in a one-dimensional simple harmonic oscillator potential. At time t = 0 it is described by the state where lo and l) are normalised energy eigenfunctions corresponding to e...
A particle with mass m is in a one-dimensional simple harmonic oscillator potential. At time t = 0 it is described by the state where lo and l) are normalised energy eigenfunctions corresponding to energies E and Ey and b and c are real constants. (a) Find b and c so that (x) is as large as possible. b) Write down the wavefunction of this particle at a time t later c)Caleulate (x) for the particle at time t (d)...
(a) (i) Discuss the eigenvalues of a quantum mechanical harmonic oscillator(QMHO). (ii) What is the significance...
(a) (i) Discuss the eigenvalues of a quantum mechanical harmonic
oscillator(QMHO).
(ii) What is the significance of the eigenfunctions of the QMHO
to be non-zero
outside the harmonic potential?
(a) (i) Discuss the eigenvalues of a quantum mechanical harmonic oscillator (QMHO). (ii) What is the significance of the eigenfunctions of the QMHO to be non-zero outside the harmonic potential? Give an example to illustrate your answer.
Find the chemical potential of a one dimensional harmonic oscillator and a two dimensional harmonic oscillator....
Find the chemical potential of a one dimensional harmonic oscillator and a two dimensional harmonic oscillator. Please show all work. Thanks!
Question A2: Coherent states of the harmonic oscillator Consider a one-dimensional harmonic oscillator with the Hamiltonian...
Question A2: Coherent states of the harmonic oscillator Consider a one-dimensional harmonic oscillator with the Hamiltonian 12 12 m2 H = -2m d. 2+ 2 Here m and w are the mass and frequency, respectively. Consider a time-dependent wave function of the form <(x,t) = C'exp (-a(x – 9(t)+ ik(t)z +io(t)), where a and C are positive constants, and g(t), k(t), and o(t) are real functions of time t. 1. Express C in terms of a. [2 marks] 2. By...
The three-dimensional harmonic oscillator Cartesian wave functions that you found in Prob. 4.46 a...
The three-dimensional harmonic oscillator Cartesian wave functions that you found in Prob. 4.46 are simultaneous eigenfunctions of H and parity (i.e., r →-r), but they are not also simultaneous eigenfunctions of L' and Lz. However, we know that it's possible to construct eigenfunctions of H for the 3D harmonic oscillator that are also eigenfunctions of L, Lz, and parity. Combine the Gaussian factors that appear in your Prob. 4.46 eigenfunctions into a function of r that is independent of θ...
Please solve with the
explanations of notations
1. The two dimensional Harmonic Oscillator has the Hamiltonian n, n'>denotes the state In> of the x-oscillator and In'> of the y-oscillator. This system is perturbed with the potential energy: Hi-Kix y. The perturbation removes the The perturbation removes the degeneracy of the states | 1,0> and |0,1> a) In first order perturbation theory find the two nondegenerate eigenstates of the full b) Find the corresponding energy eigenvalues. На Hamiltonian as normalized linear...
3. Anharmonicity (6 marks] Consider the three-dimensional isotropic harmonic oscillator 2 1 242 рґ which has energy eigenvalues En-hu(n+3/2), where n- 0,1,2.. (a) Calculate the first-order shift in the ground-state energy of the harmonic oscillator due to the addition of an anharmonic term C24 to the potential, where C> 0. (b) Calculate instead the first-order shifts in the energies of the n - 1 ercited states due to the addition of the anharmonic term C (c) For the lowest energy...
Will Rate!
Please write clearly, thank you
Problem 30: 2D harmonic Oscillator (6 pts Setup the Hamilton-Jacobi Differntial equation in cartesian coordinates for the 2-dimensional harmonic oscillator and solve it. Find x(t) and y(t)
Problem 30: 2D harmonic Oscillator (6 pts Setup the Hamilton-Jacobi Differntial equation in cartesian coordinates for the 2-dimensional harmonic oscillator and solve it. Find x(t) and y(t)
Problem 4.39 Because the two-dimensional harmonic oscillator potential is spherically symmetric, the Schrödinger equation can be handled by separation of variables in spherical coordinates, as well as cartesian coordinates. Use the power series method to solve the radial equation. Find the recursion formula for the coefficients, and determine the allowed energies. Check your answer
Problem 4.39 Because the two-dimensional harmonic oscillator potential is spherically symmetric, the Schrödinger equation can be handled by separation of variables in spherical coordinates, as well...
A particle of mass m is bound by the spherically-symmetric three-dimensional harmonic- oscillator potential energy , and ф are the usual spherical coordinates. (a) In the form given above, why is it clear that the potential energy function V) is (b) For this problem, it will be more convenient to express this spherically-symmetric where r , spherically symmetric? A brief answer is sufficient. potential energy in Cartesian coordinates x, y, and z as physically the same potential energy as the...
A particle with mass m is in a one-dimensional simple harmonic oscillator potential. At time t = 0 it is described by the state where lo and l) are normalised energy eigenfunctions corresponding to energies E and Ey and b and c are real constants. (a) Find b and c so that (x) is as large as possible. b) Write down the wavefunction of this particle at a time t later c)Caleulate (x) for the particle at time t (d)...
(a) (i) Discuss the eigenvalues of a quantum mechanical harmonic
oscillator(QMHO).
(ii) What is the significance of the eigenfunctions of the QMHO
to be non-zero
outside the harmonic potential?
(a) (i) Discuss the eigenvalues of a quantum mechanical harmonic oscillator (QMHO). (ii) What is the significance of the eigenfunctions of the QMHO to be non-zero outside the harmonic potential? Give an example to illustrate your answer.
Question A2: Coherent states of the harmonic oscillator Consider a one-dimensional harmonic oscillator with the Hamiltonian 12 12 m2 H = -2m d. 2+ 2 Here m and w are the mass and frequency, respectively. Consider a time-dependent wave function of the form <(x,t) = C'exp (-a(x – 9(t)+ ik(t)z +io(t)), where a and C are positive constants, and g(t), k(t), and o(t) are real functions of time t. 1. Express C in terms of a. [2 marks] 2. By...
The three-dimensional harmonic oscillator Cartesian wave functions that you found in Prob. 4.46 are simultaneous eigenfunctions of H and parity (i.e., r →-r), but they are not also simultaneous eigenfunctions of L' and Lz. However, we know that it's possible to construct eigenfunctions of H for the 3D harmonic oscillator that are also eigenfunctions of L, Lz, and parity. Combine the Gaussian factors that appear in your Prob. 4.46 eigenfunctions into a function of r that is independent of θ...
Most questions answered within 3 hours.
-
IN PYTHON ONLY !! Program 2: Re-work
program #5 (WeeklyHours) from the previous assignment such that...
asked 23 minutes ago -
The average length of time between arrivals at a turnpike
toll-booth is 26 seconds. What is...
asked 2 hours ago -
(a) A piston at 6.1 atm contains a gas that occupies a volume of
3.5 L....
asked 3 hours ago -
Please answer true or false. Words
cannot be changed or added in to make it true...
asked 3 hours ago -
An empty test tube weighs 15.923 grams. Then,
MgCl2•6H2O is added into the test tube. After...
asked 3 hours ago -
Assume memory access is 10 units of time and disk access is
10000 units of time....
asked 3 hours ago -
1. Are all good samples random?
2. Magazines often report surveys giving statistics such as “63%...
asked 3 hours ago -
Under all the various types of market structures, firms
must eventually earn some economic profits for...
asked 3 hours ago -
Consider the following fitness regime for a single locus trait
with two co-dominant alleles: w11 =...
asked 3 hours ago -
A large cable company reports the following.
80% of its customers subscribe to its cable TV...
asked 4 hours ago -
Please answer the question in brief.
Discuss the role of ERP in organizations. Are ERP tools...
asked 3 hours ago -
Discuss the pros and cons of collaborative software such
as SameTime. Does it increase productivity? What...
asked 3 hours ago