Question

A particle is incident upon a square barrier of height
*U* and width *L* and has *E* = *U*.
What is the probability of transmission? You must show all
work.

Answer #1

A square barrier of height Vo = 5.0 eV and width of a = 1.0nm
has a beam of electrons incident on it having kinetic energy E =
4.0 eV. The wave function for x less than or equal to 0 can be
written, Psi1 = Aeik1x +
Be-ik1x and for the region inside the
barrier, the wave function can be written Psi2 =
Cek2x + Dek2x.
Determine the equations describing the continuity conditions at
x=0.

An electron having total energy E = 3.40 eV approaches
a rectangular energy barrier with U = 4.10 eV and
L = 950 pm as shown in the figure below. Classically, the
electron cannot pass through the barrier because E <
U. Quantum-mechanically, however, the probability of
tunneling is not zero.
(a) Calculate this probability, which is the transmission
coefficient. (Use 9.11 10-31 kg for the mass
of an electron, 1.055 10-34 J · s for ℏ, and
note that there are...

1.Consider a particle in a square potential barrier with E =
0.750 Vo and another particle with E = 0.250 Vo. Vo is the height
of the barrier. Which of these two particle is more likely to
experience tunneling?
2.Estimate the velocity and kinetic energy of neutrons needed to
study the atomic structure of a material if their wavelength is of
the order of 2 Å.

1. A beam of protons of energy 3.75 MeV is incident on a barrier
of height 18.00 MeV and
thickness 1.65 fm (1.65 x 10^ -15 m). (a) What is the probability
of the protons tunneling through the barrier?
(b) By what factor does the probability change if the barrier
thickness is doubled ?

A particle is confined to the one-dimensional infinite potential
well of width L. If the particle is in the
n=2 state, what is its probability of detection between a) x=0, and
x=L/4; b) x=L/4, and x=3L/4; c) x=3L/4,
and x=L? Hint: You can double check your answer if you calculate
the total probability of the particle being
trapped in the well.
Please answer as soon as possible.

1 - Write the one dimensional, time-independent Schrödinger
Wave Equation (SWE). Using the appropriate potential energy
functions for the following systems, write the complete time
independent SWE for:
(a) a particle confined to a one-dimensional infinite square
well,
(b) a one-dimensional harmonic oscillator,
(c) a particle incident on a step potential, and
(d) a particle incident on a barrier potential of finite width.
2 - Find the normalized wavefunctions and energies for the
systems in 1(a). Use these wavefunctions to...

A 15 MeV a particle (mass 3730 MeV/c^2) is approaching a heavy
nucleus head on. Approximate the Coulomb repulsion between the a
and the nucleus by the square barrier of height 20 MeV and width 10
fm. What is the probability the a particle tunnels into the
nucleus?
A. 7e-12
B. .016
C. 9e-9
D. 16e-4

A proton and a deuteron (which has the same charge as the
proton but 2.0 times the mass) are incident on a barrier of
thickness 10.5 fm and “height” 11.1 MeV. Each particle has a
kinetic energy of 2.80 MeV.
a.) Which particle has the higher probability of tunneling
through the barrier?
a. Photon
b. none of them will pass through the
barrier
c. both have same probability
b. What is the ratio of the tunneling probability...

A box with an open top has a square base and four sides of equal
height. The volume of the box is 225 ft cubed. The height is 4 ft
greater than both the length and the width. If the surface area is
205 ft squared. what are the dimensions of the box?
What is the width of the box?.
What is the length of the box?

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...

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