Answered: Consider the motion of a classical… | bartleby

Related questions

Question

Consider the motion of a classical particle in a
one dimensional double-well
potential V(x)
1
(x? – 2). If the particle is displaced infinitesimally from the minimum
on the x-axis (and friction is neglected), then

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

I need the answer as soon as possible
Be *(1) the position operator for a particle subjected to a potential of a one-dimensional harmonic oscillator P mox (Ĥ =+ 2m 2 Evaluate [î(t),î(0)] Heisenberg's chart in
Demonstrate that e#ikz are solutions to both H and p, (momentum) for a free particle. Do you expect a difference for a bound particle where V (z) + 0?
a) Show explicitly (by calculation) that the <p> = <p>* is fulfilled for the expectation value of themomentum. b) The three expressions xp, px and (xp+px)/2 are equivalent in classical mechanics.Show that for corresponding quantum mechanical operators in the orders shown, that <Q> = <Q>* isfulfilled by one of these operators, but not by the other two.
v (z, t) is a solution of the Schrödinger equation for a free particle of mass m in one dimension, and v (z, 0) = A exp (-z²/a²). (a) At time t = 0 find the probability amplitude in momentum space. (b) Find (x, t).
Be-H is given -ur In the Born approximation, the scattering amplitude f(e) for the Yukawa potential V(r) = by: (in the following b = 2k sin E = h?k? / 2m) 2 | 2mß 2mß 2mß 2mB (a) (b) (c) (d) h? (u? +b?)
When a particle of energy E approaches a potential barrier of height V0, where E >> V0, show that the refl ection coeffcient is about {[V0 sin(kL)]/2E} 2
Consider the one-dimensional step-potential V (x) = {0 , x < 0; V0 , x > 0}(a) Calculate the probability R that an incoming particle propagating from the x < 0 region to the right will reflect from the step.(b) Calculate the probability T that the particle will be transmitted across the step.(c) Discuss the dependence of R and T on the energy E of the particle, and show that always R+T = 1.[Hints: Use the expression J = (-i*hbar / 2m)*(ψ*(x)ψ′(x) − ψ*'(x)ψ(x)) for the particle current to define current carried by the incoming wave Ji, reflected wave Jr, and transmitted wave Jt across the step.For a simple plane wave ψ(x) = eikx, the current J = hbar*k/m = p/m = v equals the classical particle velocity v. The reflection probability is R = |Jr/Ji|, and the transmission probability is T = |Jt/Ji|. You need to write and solve the Schrodinger equation in regions x < 0 and x > 0 separately, and connect the solutions via boundary conditions at x = 0 (ψ(x) and ψ′(x) must be…
If the Hamiltonian of the one-dimensional classical harmonic oscillator is given by H(p2/2m) +(½)mw? x², this oscillator's a) the partition function b) Helmholtz free energy cc) Average energy
We can use a quartic function function to represent this potential as shown below. Using the first order perturbation theory for particle in a box, calculate the ground- state energy: V(2) = ca 0< x < b a. How large of an effect on the energy is the perturbation of a curved wall?
Let's say we have a particle in motion. If f(x) represents the function of the particle's velocity, what does the integral of f(x) represent?
Q.3) (30 Points) For the harmonic oscillator, the position and momentum operators are given by (a* + a) and p = i 2mw mwh (a*- a¯), respectively. X = Using the relations a* |n) = Vn + 1 |n + 1) and a |n) = Vn |n – 1); a) Find the expectation value of (xp). (n|xp|n) =? b) Find the expectation value of (x³). (n|x3|n) =? Please answer questions by showing all steps in your calculations clearly and easy to read and understandable.

SEE MORE QUESTIONS