Question

A beam of particles is incident from the negative *x*
direction on a potential energy step at *x* = 0. When
*x* < 0, the potential energy of the particles is zero,
and for *x* > 0 the potential energy has the constant
positive value *U*_{0}. In the region *x*
< 0, the particles have a kinetic energy *K* that is
smaller than *U*_{0}. What should the form of the
wave function be in the region *x* > 0?

Answer #1

Particles with energy E, are incident from the left, on the
step-potential of height V0 = 2E as shown: a. What are the wave
numbers in the two regions, 1 k and 2 k , in terms of E? b. Write
down the most general solutions for the Schrodinger Equation in
both regions? Identify, with justification, if any of the
coefficients are zero. c. Write down the equations that result for
applying the boundary conditions for the wave functions at...

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?...

A beam of electrons, each with energy E=0.1V0 , is incident on a
potential step with V0 = 2 eV. This is of the order of magnitude of
the work function for electrons at the surface of metals. Calculate
and graph (at least 5 points) the relative probability |Ψ2|^2 of
particles penetrating the step up to a distance x = 10-9 m, or
roughly five atomic diameters. (Hint: assume A=1.)

A beam of protons, each with energy E=20 MeV, is incident on a
potential step 40 MeV high. Graph using a computer the relative
probability of finding protons at values of x > 0 from x = 0 to
x = 5 fm.
Please do not just copy the answer to this question that has
been posted on Chegg all ready

Reflection from a Step with E < V0: A beam of electrons, each
with energy E=0.1V0 , is incident on a potential step with V0 = 2
eV. This is of the order of magnitude of the work function for
electrons at the surface of metals. Calculate and graph (at least 5
points) the relative probability |Ψ#|# of particles penetrating the
step up to a distance x = 10-9 m, or roughly five atomic diameters.
(Hint: assume A=1.)

When a particle of energy E hits the boundary of a step
potential of potential V0>0 at x=0, when is the probability that
it will get reflected greater than 0 (that is, R>0)?
A.Always
B.Only if E>V0
C.Only if the potential step is positive (that is, V=0 for
x<0, V=V0 for x>0)
D.Only if the potential step is negative (that is, V=V0 for
x<0, V=0 for x>0)
E.Never
Only if E<V0

A beam of electrons with kinetic energy 25 eV encounter a
potential barrier of height 20 eV. Some electrons reflect from the
barrier, and some are transmitted. Find the wave number k of the
transmitted electrons.
You can take U = 0 for x < 0, and U = 15 eV for x > 0

A beam of charged particles consisting of electron and protons
are moving in +x direction and enter a region of uniform magnetic
field in +y direction. If the protons are deflected in radius of
9.75ₓ10-2 m radius, calculate
a) The magnitude of the magnetic field
b) The radius that electron will be deflected and draw the
schematic of the problem.
c) The electric field that should be applied so that the protons
remain undeflected (both magnitude and direction)

Which of the following statements is/are true regarding
behaviors of charged particles inside electric field?
Positive charges are accelerated by electric fields toward
points at higher electric potential;
If the electric field at a certain region is zero, then the
electric potential at the same region is constant;
If a negative charge moves in the direction of the electric
field, the field does positive work and the potential energy
increases
If a positive charge moves opposite to the electric field,...

Probably still from our high-school days, we all remember the
rules of reflection and refraction of light at a plane interface,
say between vacuum and a medium with refractive index n:
α = α ′, sin α/ sin β = n. (3)
Here we denoted the incident angle as α, the reflection angle α
′ and the refraction angle β. It is interesting to see if we have a
similar situation for material quantum-mechanical waves. For this
purpose, let us...

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