A particle with mass m and energy E is moving in one-dimension
from right to legt....
A particle with mass m and energy E is moving in one-dimension
from right to legt. It is incident on the step potential V(x)=0 for
x<0 nd V(x)=V0 for x>0 where E>V0>0. Find the
reflection coefficient R in terms of m,E and V0, and h-bar.
Problem 1: The energy E of a particle of mass m moving at speed
v is given by: E2 = m2 c4 + p2 c2 (1) p=γmv (2) 1 γ = 1−v2/c2 (3)
This means that if something is at rest, it’s energy is mc2. We can
define a kinetic energy to be the difference between the total
energy of an object given by equation (1) and the rest energy mc2.
What would be the kinetic energy of a baseball...
A particle of mass ? moves in one dimension along the ?- axis.
Its potential energy is given by ?(?) = ??3 − ??, where ? and ? are
positive constants.
(a) Calculate the force on the particle, ?(?). Find the
position of all equilibrium points and identify them as stable or
unstable.
(b) Draw an energy diagram showing the potential energy U, the
kinetic energy K, and the total mechanical energy E for bound
motion. Show the location of...
3) The momentum eigenfunction for a particle moving in one
dimension is фр--h-1/2eipz/n The energy eigenfunction for a
particle in a 1D box of length L is u()- is expanded in terms of
фе(x), the expansion coefficient may be interpreted as the momentum
probability amplitude; its square gives the probability density for
momentum. Determine the momentum probability density for u(x)
One particle whose mass is defined by m is moving along a
certain line in the region x>0 is subjected to a conservative
net force given by the following equation: F(x)= F₀x eˣ^²/²ᴸ^²
The constants F and L are both positive real quantities with
appropriate physical dimensions.
Find the formula for the corresponding U(x), with the given
assumption that the limₓ↠∞U(x)=0.
Secondly, we know that the particle is launched from an initial
location x₀>>>L towards x=0. (the >>> mean that...
Solve for the motion of a free particle moving in one dimension
with initial position and initial momentum using Hamilton –Jacobi
theory. Please be sure to use the fact that the resulting
Kamiltonian vanishes to simplify your work. Comment on the results
you find.
Classical mechanics - upper level
task 1. A particle of mass m, in one dimension, moves in the
field of force constant F.
Canonical transformation is:
q (t) → Q (t) = q (t + τ) p (t) → P (t) = p (t + τ) (1)
Find the derivative function F2 (q, P) ,
then linearize it by keeping only the linear contributions in
τ.
Shoe that f2 (q, P), the contribution within F2 that multiplies
τ corresponds to...
A moving particle of mass M and impulse P breaks down in two
fragments. One of these has a mass m1=1.00 MeV/c2 and an impulse
p1 = 1.75Mev/c in the +x direction. The other one has a mass m2 =
1.50 MeV/c2 and an impulse p2 = 2.005 MeV/c in the +y direction.
Find: a) The initial impulse (value and direction) b) Total energy
of the initial particle c) The mass M of the initial particle d)
The value of...
A block of mass m= 5.00-kg is moving to the right with a speed
of v= 2.00 m/son a horizontal,frictionless surface. The block
encounters a relaxed(that is, neither compressed nor
extended)spring with spring constant k= 2,000.00 N/m.
a.What is the kinetic energy of the block before hitting the
spring?
b.What is the kinetic energy of the block when the spring is at
maximum compression?
c.How much energy is stored in the spring at maximum
compression?
d.How far does the spring...
3. Suppose a beam of particles of mass m and kinetic energy E is
incident from the left on a potential well given by:
U(x) = ?U0 (for 0 < x < L where U0
> 0)
U(x) = 0 ( otherwise )
(a) What is the Schrodinger Wave Equation (S.W.E.) for the
region x < 0 ? (Hint: include both incident and reflected
waves)
(b) What is the S.W.E. for the region x > L ? (Hint: this
will...
4. Hamiltonian equations of motion A particle of mass m moving
in two dimensions has the Hamiltonian H(x, y, px, py) = (px − cy)
^2 + (py + cx)^ 2 /2m where c is a constant. Find the equations of
motion for x, y, px, py. Use these to write the equations of motion
for the complex variables ζ = x + iy and ρ = px + ipy. Eliminate ρ
to show that m¨ζ − 2ic ˙ζ =...