Question

Write down the Hamiltonian operator Hˆ for a single particle of mass m in 1 dimension...

Write down the Hamiltonian operator Hˆ for a single particle of mass m in 1 dimension in a potential U(x). Identify the term that represents kinetic energy. Identify the term that represents potential energy.

Science   Advanced-Physics   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Let's start from the definition, Hamiltonian is the sum of Kinetic energy and Potential energy.

So we have,

Since the particle is of mass "m" and in one dimension we can write Kinetic energy as-

And Potential energy can be written as-

We know in Quantum mechanics, we write momentum operator in one dimension (so it only depends on x) as-

So, our final form of Hamiltonian operator becomes-

Here first term represents Kinetic energy and the second term represents the potential energy.

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
9. Write down the Hamiltonian operator in Cartesian coordinates for the hydrogen atom. Identify each term.  
9. Write down the Hamiltonian operator in Cartesian coordinates for the hydrogen atom. Identify each term.  
a particle of mass m moves in three dimension under the action of central conservative force...
a particle of mass m moves in three dimension under the action of central conservative force with potential energy v(r).find the Hamiltonian function in term of spherical polar cordinates ,and show φ,but not θ ,is ignorable .Express the quantity J2=((dθ/dt)2 +sin2 θ(dφ /dt)2) in terms of generalized momenta ,and show that it is a second constant of of the motion
Let us consider a particle of mass M moving in one dimension q in a potential...
Let us consider a particle of mass M moving in one dimension q in a potential energy field, V(q), and being retarded by a damping force −2???̇ proportional to its velocity (?̇). - Show that the equation of motion can be obtained from the Lagrangian: ?=?^2?? [ (1/2) ??̇² − ?(?) ] - show that the Hamiltonian is ?= (?² ?^−2??) / 2? +?(?)?^2?? Where ? = ??̇?^−2?? is the momentum conjugate to q. Because of the explicit dependence of...
A particle with a mass m = 2.00 kg is moving along the x axis under...
A particle with a mass m = 2.00 kg is moving along the x axis under the influence of the potential energy function U(x) = (2.00 J/m2)x2 − 32.0 J. If the particle is released from rest at the position x = 6.40 m, determine the following. (The sign is important. Be sure not to round intermediate calculations.) (a) total mechanical energy of the particle at any position: =_____ J. (b) potential energy of the particle at the position x...
For a particle of mass 3.0 x 10-23 Kg, in a box of equal dimension 5.0...
For a particle of mass 3.0 x 10-23 Kg, in a box of equal dimension 5.0 Å, find the probability that the particle is in a region of 1.0 Å in the center of the box. The energy of the particle is 6.58 x 10-26 J.
A particle of mass, m, in an isolated environment moves along a line with speed v...
A particle of mass, m, in an isolated environment moves along a line with speed v whilst experiencing a force proportional to its distance from the origin. a) Determine the Langrangian of the system b) Determine the Hamiltonian of the system c) Write down Hamilton’s equations of motion for the particle d) Show that the particle executes simple harmonic motion
A single conservative force acts on a 5.00 kg particle. The equation Fx = (2x +...
A single conservative force acts on a 5.00 kg particle. The equation Fx = (2x + 4) N describes this force, where x is in meters. As the particle moves along the x axis from x = 3.00 m to x = 7.00 m, calculate the following. (a) the work done by this force on the particle J (b) the change in the potential energy of the system J (c) the kinetic energy the particle has at x = 7.00...
A particle of mass m is projected with an initial velocity v0 in a direction making...
A particle of mass m is projected with an initial velocity v0 in a direction making an angle α with the horizontal level ground as shown in the figure. The motion of the particle occurs under a uniform gravitational field g pointing downward. (a) Write down the Lagrangian of the system by using the Cartesian coordinates (x, y). (b) Is there any cyclic coordinate(s). If so, interpret it (them) physically. (c) Find the Euler-Lagrange equations. Find at least one constant...
(a) One particle has mass m and a second particle has mass 2m. The second particle...
(a) One particle has mass m and a second particle has mass 2m. The second particle is moving with speed v and the first with speed 2v. How do their kinetic energies compare? (b) A person drops a pebble of mass m1 from a height h, and it hits the floor with kinetic energy K. The person drops another pebble of mass m2 from a height of 2h, and it hits the floor with the same kinetic energy K. How...
Particles of mass m are incident from the positive x axis (moving to the left) onto...
Particles of mass m are incident from the positive x axis (moving to the left) onto a potential energy step at x=0. At the step the potential energy drops from the positive value U_0 for all x>0 to the value 0 for all x<0. The energy of the particles is greater than U_0. A) Sketch the potential energy U(x) for this system. B) How would the wavelength of a particle change in the x<0 region compared to the x>0 region?...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT