Consider a traveling (electrons) wave moving in the +x direction
approaching a step barrier of height 1 eV; that is V = 0 for x <
0, V = 1.0 eV for x ≥ 0. For x < 0, there will be both the
traveling wave in the +x direction. For x ≥ 0, only a solution
corresponding to motion in the +x direction exists. By solving the
Schrödinger wave equation in both x < 0 and x ≥ 0 regions, and
requiring that the two solutions join smoothly at x = 0 (that is,
both magnitudes and slopes for the solutions are equal at x = 0),
calculate the reflection coefficient R with (a) E = 1.1 eV and (b)
E = 0.9 eV, if R = |Ψrefl| 2 /|Ψinc| 2 . (c) What is R for E = 1.1
eV for a wave traveling in the -x direction from x ≥ 0? (d) If T is
the transmission coefficient, then R + T = 1. Fore E = 1.1 eV, you
know R and can calculate T. You will find that T is not given by
|Ψtrans| 2 /|Ψinc| 2 . Explain.
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Consider a traveling (electrons) wave moving in the +x direction approaching a step barrier of height 1 eV; that is V =...
1. Consider an electron initially moving in the positive x-direction along the negative x-axis wi...
1. Consider an electron initially moving in the positive x-direction along the negative x-axis with an energy E. At the origin the potential energy U (x) changes abruptly, from U(x) = 0 for x < 0, to U(x) = 1.00 eV for x > 0. If E=1.02 eV, just higher than the barrier by 2%, what is the barrier penetration length? What is the reflectance? What is the transmittance? 2. Consider an electron initially moving in the positive x-direction along...
8a: a light wave of amplitude E sub 0 = 1 traveling in the +z direction...
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Consider the Semiconductor above in Figure 1. For electrons traveling along the [111] Direction which energy...
Consider the Semiconductor above in Figure 1.
For electrons traveling along the [111] Direction which energy
valley has the greatest effective mass?
Consider two electrons one located in the X-valley and one in
the L-Valley, which one would have the greater velocity
magnitude?
What compound semiconductor material is shown above in Figure
1, is it a direcot or indirect gap semiconductor?
Energy 300K Eg- 1.42 eV EL = 1.71 eV Ex=1.90 eV Eso 0.34 eV , X-valley .alley L-valley <100>...
(III) Quantum Tunneling Consider an electron in 1D in presence of a potential barrier of width...
(III) Quantum Tunneling Consider an electron in 1D in presence of a potential barrier of width L represented by a step function ſo I<0 or 1>L V U. r>0 and 2<L The total wavefunction is subject to the time-independent Schrödinger equation = EV (2) 2m ar2 +V where E is the energy of the quantum particle in question and m is the mass of the quantum particle. A The total wavefunction of a free particle that enters the barrier from...
mechani mie The potential energy barrier shown below is a simplified model of thec electrons in...
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An electromagnetic wave traveling in the -x direction in vacuum has a frequency 2x1014Hz. The electric...
An electromagnetic wave traveling in the -x direction in vacuum
has a frequency 2x1014Hz. The electric field in the wave has
maximum value of 2 V/m. If we define the time and position such
that the electric field has maximum value at position x=0 at
time=0, a possible equation describing the electric field is:
"⃗
a. ?=(2V/m)sin[(4.2x106 /m)x-(1.3x1015Hz)t]?̂
"⃗ ' b. ?=(2V/m)cos[(4.2x106 /m)x+(1.3x1015Hz)t]?
"⃗ ' c. ?=(1V/m)sin[(1.3x1015 /m)x-(4.2x106Hz)t]?
"⃗
d. ?=(4V/m)cos[(4.2x106 /m)x+(1.3x1015Hz)t]?̂
2. An electromagnetic wave traveling in the -x...
F(x)=2/(x^4+1). Write the equation y(x,t) for a wave traveling in the -x direction with velocity v=20...
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Consider a particle incident from the left on the potential step. Where E = 2 eV...
Consider a particle incident from the left on the potential step. Where E = 2 eV V(x) {5 eV lo x < 0 x > 0 1) Find the wave function of the particle in two regions 2) Find reflection and transmission coefficients R and T
A sinusoidal transverse wave is traveling along a string in the negative direction of an x...
A sinusoidal transverse wave is traveling along a string in the
negative direction of an x axis. The figure below shows a
plot of the displacement as a function of position at time
t = 0. The x axis is marked in increments of 10
cm and the y axis is marked in increments of 2 cm. The
string tension is 3.1 N, and its linear density is 34 g/m.
(a) Find the amplitude.
m
(b) Find the wavelength.
m...
Wave function You are observing a wave traveling along the x-axis. The first picture (y vs....
Wave function
You are observing a wave traveling along the x-axis. The first picture (y vs. x) shows a snapshot of the wave at t=0. The second picture dy vs. t) shows how the wave height varies in time from the perspective of an observer standing at fixed location x-0. From this information, determine if the wave is traveling to the left or right. Give a one-sentence explanation justifying your answer 2) 3) The wave function for a harmonic (i.e.,...
Consider the Semiconductor above in Figure 1.
For electrons traveling along the [111] Direction which energy
valley has the greatest effective mass?
Consider two electrons one located in the X-valley and one in
the L-Valley, which one would have the greater velocity
magnitude?
What compound semiconductor material is shown above in Figure
1, is it a direcot or indirect gap semiconductor?
Energy 300K Eg- 1.42 eV EL = 1.71 eV Ex=1.90 eV Eso 0.34 eV , X-valley .alley L-valley <100>...
(III) Quantum Tunneling Consider an electron in 1D in presence of a potential barrier of width L represented by a step function ſo I<0 or 1>L V U. r>0 and 2<L The total wavefunction is subject to the time-independent Schrödinger equation = EV (2) 2m ar2 +V where E is the energy of the quantum particle in question and m is the mass of the quantum particle. A The total wavefunction of a free particle that enters the barrier from...
mechani mie The potential energy barrier shown below is a simplified model of thec electrons in metals. The metal workfunction (Ew), the minimum energy required to remove an electron from the metal, is given by Ew-,-E where 1s the height of the potential energy barrier and E is the energy of the electrons near the surface of the metal. The potential energy barrier is = 5 eV V(x) V=0 (a) The wavefunction of an electron on the surface (x< 0)...
An electromagnetic wave traveling in the -x direction in vacuum
has a frequency 2x1014Hz. The electric field in the wave has
maximum value of 2 V/m. If we define the time and position such
that the electric field has maximum value at position x=0 at
time=0, a possible equation describing the electric field is:
"⃗
a. ?=(2V/m)sin[(4.2x106 /m)x-(1.3x1015Hz)t]?̂
"⃗ ' b. ?=(2V/m)cos[(4.2x106 /m)x+(1.3x1015Hz)t]?
"⃗ ' c. ?=(1V/m)sin[(1.3x1015 /m)x-(4.2x106Hz)t]?
"⃗
d. ?=(4V/m)cos[(4.2x106 /m)x+(1.3x1015Hz)t]?̂
2. An electromagnetic wave traveling in the -x...
Consider a particle incident from the left on the potential step. Where E = 2 eV V(x) {5 eV lo x < 0 x > 0 1) Find the wave function of the particle in two regions 2) Find reflection and transmission coefficients R and T
A sinusoidal transverse wave is traveling along a string in the
negative direction of an x axis. The figure below shows a
plot of the displacement as a function of position at time
t = 0. The x axis is marked in increments of 10
cm and the y axis is marked in increments of 2 cm. The
string tension is 3.1 N, and its linear density is 34 g/m.
(a) Find the amplitude.
m
(b) Find the wavelength.
m...
Wave function
You are observing a wave traveling along the x-axis. The first picture (y vs. x) shows a snapshot of the wave at t=0. The second picture dy vs. t) shows how the wave height varies in time from the perspective of an observer standing at fixed location x-0. From this information, determine if the wave is traveling to the left or right. Give a one-sentence explanation justifying your answer 2) 3) The wave function for a harmonic (i.e.,...
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