Answered: (3) Consider the Hamiltonian given as H… | bartleby

Related questions

Question

(3) Consider the Hamiltonian given as Ĥ = + + Fx , where each term has a clear physical meaning.
2m 2
Specifically, we have a particle in a harmonic potential energy subjected to a uniform external force F. What
is the energy spectrum of this Hamiltonian? Explain why the result makes sense and use a sketch of the
potential energy as a function of x. Hint: Complete the square, and use problem 2 as a guide.

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 5 steps with 5 images

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

This problem is designed to give you practice using the Dirac delta function. Eval- uate the following integrals. Show your reasoning.
For Problem 8.37, how do I find <1/r> within the integral? I think that the exponent function inside of P(r) is actually troublesome to finding what I need to find; however, I am not certain of what's really the correct procedure here.
(a) Show that the sum of two hermitian operators is hermitian. (b) Suppose Ô is hermitian, and a is a complex number. Under what condition (on a) is a Q hermitian? (c) When is the product of two hermitian operators hermitian? (d) Show that the position operator (f = x) and the hamiltonian operator (H = -(h2/2m)d²/dx2? + V (x)) are hermitian.
Using the eigenvectors of the quantum harmonic oscillator Hamiltonian, i.e., n), find the matrix element (6|X² P|7).
Need full detailed answer.
5. Consider the two state system with basis |+) which diagonalizes the Pauli matrix 03. Generally the state of the system at time t can be written as |W(t)) = c+(t)|+) + c_(t)|-). (i) For the Hamiltonian of the system, first take H = functions c+(t) given the initial condition that at time t = 0 Eo03. Solve for the coefficient |W(0)) = |-).
The Hamiltonian of an electron of mass m in a constant electric field E in one dimension can be written as Ĥ=+eEx where â and are the position and momentum operators, respectively. With initials conditions (t = 0) = 0 and p(t = 0) = 0, which one of the following gives (t) at time in the Heisenberg picture? You may use the commutator [â,p] = iħ. O a. O b. eEt2 2m O C. e Et O d. -eEt O e. eEt² m pt m