Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
expand_more
expand_more
format_list_bulleted
Question
Chapter 5, Problem 77CE
(a)
To determine
Introduction:
For infinite potential well the distance between the two levels is increased as the energy increases, as the energy is proportional to
(b)
To determine
For infinite potential well the distance between the two levels is increased as the energy increases, as the energy is proportional to
(c)
To determine
Whether the characteristic is shared by
(d)
To determine
Whether the characteristic is shared by
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
1
1
For a simple harmonic oscillator potential, Vo(x) =kx² = mo'x?,
%|
2
ħo
and the ground state
2
the ground state energy eigenvalue is E
eigenfunction is
a²x?
то
exp
where a?
%3D
2
Now suppose that the potential has a small perturbation,
1
kx² →
1
-kx? + λxό.
2
Vo(x):
→ V(x) =
Use perturbation theory to find the (first order) corrected eigenvalue, in terms of @.
[7]
1x 3 x 5 x ...× (2n – 1)
2n+1Bn
You will need:
x2" exp(-ßx²) dx =
An electron trap in an
infinite potential
Well
length 2.0o nm
Electron Can be
considered as
free particle - having particle
and
4(x)=Asin
UIS
> x>0
品)
11
UIS
7.
11
X.
xp
find the probabiliy of Kinetic energy
between
77x>O
Schro
the
x >0
umop
nger
uation for the electron in
infante potential well
We can approximate an electron moving in a nanowire (a small, thin wire) as a one-dimensional infi nite square-well potential. Let the wire be 2.0 μm long. The nanowire is cooled to a temperature of 13 K, and we assume the electron’s average kinetic energy is that of gas molecules at this temperature ( 3kT/2). (a) What are the three lowest possible energy levels of the electrons? (b) What is the approximate quantum number of electrons moving in the wire?
Chapter 5 Solutions
Modern Physics
Ch. 5 - Prob. 1CQCh. 5 - Prob. 2CQCh. 5 - Prob. 3CQCh. 5 - Prob. 4CQCh. 5 - Prob. 5CQCh. 5 - Prob. 6CQCh. 5 - Prob. 7CQCh. 5 - Prob. 8CQCh. 5 - Prob. 9CQCh. 5 - Prob. 10CQ
Ch. 5 - Prob. 11CQCh. 5 - Prob. 12CQCh. 5 - Prob. 13CQCh. 5 - Prob. 14CQCh. 5 - Prob. 15CQCh. 5 - Prob. 16CQCh. 5 - Prob. 17CQCh. 5 - Prob. 18CQCh. 5 - Prob. 19ECh. 5 - Prob. 20ECh. 5 - Prob. 21ECh. 5 - Prob. 22ECh. 5 - Prob. 23ECh. 5 - Prob. 24ECh. 5 - Prob. 25ECh. 5 - Prob. 26ECh. 5 - Prob. 27ECh. 5 - Prob. 28ECh. 5 - Prob. 29ECh. 5 - Prob. 30ECh. 5 - Prob. 31ECh. 5 - Prob. 32ECh. 5 - Prob. 33ECh. 5 - Prob. 34ECh. 5 - Prob. 35ECh. 5 - Prob. 36ECh. 5 - Prob. 37ECh. 5 - Prob. 38ECh. 5 - Prob. 39ECh. 5 - Prob. 40ECh. 5 - Prob. 41ECh. 5 - Prob. 42ECh. 5 - Obtain expression (5-23) from equation (5-22)....Ch. 5 - Prob. 44ECh. 5 - Prob. 45ECh. 5 - Prob. 46ECh. 5 - Prob. 47ECh. 5 - Prob. 48ECh. 5 - Prob. 49ECh. 5 - Prob. 50ECh. 5 - Prob. 51ECh. 5 - Prob. 52ECh. 5 - Prob. 53ECh. 5 - Prob. 54ECh. 5 - Prob. 55ECh. 5 - Prob. 56ECh. 5 - Prob. 57ECh. 5 - Prob. 58ECh. 5 - Prob. 59ECh. 5 - Prob. 60ECh. 5 - Prob. 61ECh. 5 - Prob. 62ECh. 5 - Prob. 63ECh. 5 - Prob. 64ECh. 5 - Prob. 65ECh. 5 - Prob. 66ECh. 5 - Prob. 67ECh. 5 - Prob. 68ECh. 5 - Prob. 69ECh. 5 - Prob. 70ECh. 5 - Prob. 71ECh. 5 - In a study of heat transfer, we find that for a...Ch. 5 - Prob. 73CECh. 5 - Prob. 74CECh. 5 - Prob. 75CECh. 5 - Prob. 76CECh. 5 - Prob. 77CECh. 5 - Prob. 78CECh. 5 - Prob. 79CECh. 5 - Prob. 80CECh. 5 - Prob. 81CECh. 5 - Prob. 82CECh. 5 - Prob. 83CECh. 5 - Prob. 84CECh. 5 - Prob. 85CECh. 5 - Prob. 86CECh. 5 - Prob. 87CECh. 5 - Prob. 88CECh. 5 - Consider the differential equation...Ch. 5 - Prob. 90CECh. 5 - Prob. 91CECh. 5 - Prob. 92CECh. 5 - Prob. 93CECh. 5 - Prob. 94CECh. 5 - Prob. 95CECh. 5 - Prob. 96CECh. 5 - Prob. 97CECh. 5 - Prob. 98CE
Knowledge Booster
Similar questions
- A particle of mass m, which moves freely inside an infinite potential well of length a, is initially in the state y(x,0)=√√3/5a sin (3xx/a)+ (1/√5a) sin (5mx/a). (a) Find y (x, t) at any later time t. Calculate the pr Lility density of thouarrow_forwarda two-dimensional, infinite-potential well lying in an xy plane that contains an electron. We probe for the electron along a line that bisects Lx and find three points at which the detection probability is maximum. Those points are separated by 2.00 nm. Then we probe along a line that bisects Ly and find five points at which the detection probability is maximum.Those points are separated by 3.00 nm.What is the energy of the electron?arrow_forwardBmoing0.15. 9:54 A docs.google.com Please use the following numbers when necessary, S4 ge p- Irdveing d y - 20 x 3rd evening. Ameng Amorning 0.1, A evening 02. B evening 0 25 rd moming -0.3. 3ed_evening -0.35 Consider a three-dimensional infinite potential well with a quantired enmy of E (n + ng + nộ). where n, 123., - 123 , 1,2.3, and a repesents the ponential well width in the x, y, and : directions i. The lowest energy level that the electron may occupy is ャ 9 2ma O Option 1 2ma O Option 6 0. O Option 5arrow_forward
- The ground state energy of a particle in a one-dimensional infinite potential well of width 1.5 nm is 20 eV. The ground state energy of the same particle in a one-dimensional finite potential well with U0 = 0 in the region 0 < x < 1.5 nm, and U0 = 50 eV everywhere else, would be greater than 50 eV. less than 20 eV. greater than 20 eV, but less than 50 eV. equal to 50 eV. equal to 20 eV.arrow_forwardAn electron is trapped in a one-dimensional infinite potential well that is 430 pm wide; the electron is in its ground state. What is the probability that you can detect the electron in an interval of width &x = 5.0 pm centered at x = 260 pm? (Hint: The interval Sx is so narrow that you can take the probability density to be constant within it.) Number i Unitsarrow_forwardQ.8: Find the center and radius of convergence of the power series 2n=1 m(n+1) (z)2n+1 Q.9: Find the McLaurin series and its radius of convergence of 3iz Q.10: Find the Laurent series that converges for 0 < I z – z,I < R and determine the precise z, = iT region of convergence: (z-in)*arrow_forward
- An electron is trapped in a one-dimensional infinite potential well that is 470 pm wide; the electron is in its ground state. What is the probability that you can detect the electron in an interval of width &x = 5.0 pm centered at x = 260 pm? (Hint: The interval 8x is so narrow that you can take the probability density to be constant within it.) Number Unitsarrow_forwardAn electron bounces elastically in 1D between two infinite potential walls separated by a distance L. The electron is in its lowest possible energy state. (a) What is the energy of this state? (b) The separation between the walls is slowly (a.k.a. 'adiabatically') increased to 2L. That the process occurs slowly means that the electron slowly adapts to continue to occupy the ground state of this new well of width 2L. What is the change in energy that the electron experiences? (c) With the walls again at a distance of L, imagine now that the separation is abruptly increased from L to 2L. This means that, at the moment when the change is made, the wavefunction is unchanged for a L. Write a (normalized) expression for 1(x) at this very moment, and draw it for the interval x = [0, 2L]. What is the expectation value of the energy for this ₁(a)? I'm calling it 1(a) not (x) to make it clear that it represents the ground state. (d) Show that the above 1(r) is no longer a solution for the…arrow_forwardAn electron is confined to move in the xy plane in a rectangle whose dimensions are Lx and Ly. That is, the electron is trapped in a two dimensional potential well having lengths of Lx and Ly. In this situation, the allowed energies of the electron depend on the quant numbers Nx and Ny, the allowed energies are given by E = H^2/8Me ( Nx^2/ Lx^2 + Ny^2/Ly^2) i) assuming Lx and Ly =L. Find the energies of the lowest for all energy levels of the electron ii) construct an energy level diagram for the electron and determine the energy difference between the second exited state and the ground state?arrow_forward
- A particle in an infinite well is in the ground state with energy1.54eV. How much energy must be added to the particle to reach the second excited state (n = 3)? The third excited state (n = 4)?arrow_forwardThe spherical symmetric potential in which a particle is moving is V(r)=Br^5, where ßis a positive constant. what is the relationship between the expectation value of kinetic andpotential energy of particle in stationary state is,arrow_forwardAn electron in a one-dimensional infinite potential well of length L has ground-state energy E1.The length is changed to L' so that the new ground-state energy is E'1 = 0.500E1 .What is the ratio L'/L?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning