Question
In: Physics
A particle of mass m is constrained to a circle of radius r0: that is, the...
A particle of mass m is constrained to a circle of radius r0: that is, the potential for the particle is 0 when the
particle is anywhere on that circle and infinite everywhere else,
?(?) = 0 (r=r0)
V(r) = ∞ (? ≠ ?0)
Find the eigenvalues and normalized eigenfunctions of the Hamiltonian for a particle on a ring.
What is the degeneracy of eigenvalues for this system. how many eigenfunctions are
there for each eigenvalue)?
Solutions
genius_generous answered 1 year agoRelated Solutions
A satellite with Mass m is in orbit with a constant radius around the earth r0...
A satellite with Mass m is in orbit with a constant radius
around the earth r0 (RE=6370km, Mass
ME = 5,98*1024kg)
a) Show that the satellite moves with uniform circular motion
and calculate the velocity v0 in dependance of G,M
E and R E .
b) At which height h above the earth's surface is the
geostationary orbit found? Which linear velocity does a satellite
have at this height?
c) Compare this to the linear velocity on earth's surface as...
A particle of mass m is constrained to lie along a frictionless, horizontal plane subject to...
A particle of mass m is constrained to lie along a frictionless,
horizontal plane subject to a force given by F (x) = −kx + kx^3/A^2
where k and A are positive constants. The particle is projected
from x = 0 to the right with initial kinetic energy T0. Find the
turning points of the motion and the condition the total energy of
the particle must satisfy if its motion is to exhibit turning
points.
A particle of mass m is constrained to lie along a frictionless, horizontal plane subject to...
A particle of mass m is constrained to lie along a frictionless,
horizontal plane subject to a force given by F (x) = −kx + kx^3/A^2
where k and A are positive constants. The particle is projected
from x = 0 to the right with initial kinetic energy T0. Find the
turning points of the motion and the condition the total energy of
the particle must satisfy if its motion is to exhibit turning
points.
A uniform disk of radius 0.543 m and unknown mass is constrained to rotate about a...
A uniform disk of radius 0.543 m and unknown mass is constrained
to rotate about a perpendicular axis through its center. A ring
with same mass as the disk\'s is attached around the disk\'s rim. A
tangential force of 0.201 N applied at the rim causes an angular
acceleration of 0.119 rad/s2. Find the mass of the disk.
A particle with mass m moves on the surface of a cylinder with radius R. At...
A particle with mass m moves on the surface of a cylinder with
radius R. At the same time, the force F = -kr on the particle
affects it through the z axis. Using the z-and θ generalized
coordinates, find the system's hamitonians. Solve the Hamilton
equation after defining the conservative quantities.
The Simple harmonic oscillator: A particle of mass m constrained to move in the x-direction only...
The Simple harmonic oscillator: A particle of mass m constrained
to move in the x-direction only is subject to a force F(x) = −kx,
where k is a constant. Show that the equation of motion can be
written in the form d^2x/dt2 + ω^2ox = 0, where ω^2o = k/m . (a)
Show by direct substitution that the expression x = A cos ω0t + B
sin ω0t where A and B are constants, is a solution and explain the...
A sphere of radius r0 = 23.0 cm and mass m = 1.20kg starts from rest...
A sphere of radius r0 = 23.0 cm and mass m = 1.20kg starts from
rest and rolls without slipping down a 36.0 ∘ incline that is 13.0
m long.
a) Calculate its translational speed when it reaches the
bottom.
b) Calculate its rotational speed when it reaches the
bottom.
c) What is the ratio of translational to rotational kinetic
energy at the bottom?
Consider a particle which is constrained to move along the surface of the sphere of radius...
Consider a particle which is constrained to move along the
surface of the sphere of radius 5, centered at the origin.
(a) If we write r(t) for the motion, write down the condition
‘constrained to move along the surface of the sphere of radius 5
centered at the origin’ in terms of r(t). (Hint. For later use, try
to get rid of square roots.)
(b) Explain why, for such a motion, we must have r 0 (t) ⊥ r(t).
(Hint....
Consider a wire of uniform density and mass M shaped into a quarter circle of radius...
Consider a wire of uniform density and mass M shaped into a
quarter circle of radius R.The wire is located in the xy plane,
with the origin at the focus of the quarter circle (i.e at the
center of the circle of which the wire is part). Choose the x axis
parallel to the line that connects the endpoints of the wire, so
that the y-z plane is a plane of reflection symmetry for the wire.
This means that the...
A particle of mass m orbits around the origin (0,0) in a circular path of radius...
A particle of mass m orbits around the origin (0,0) in a
circular path of radius r.
(a) Write the classical Hamiltonian (energy) of this system in
terms of angular momentum of the particle.
(b) Write the Schrodinger equation for this system.
(c) Find the energy eigenvalues and their corresponding
(normalized) wavefunctions.
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